My cutoff is if any of the structural wood is wiped out (i.e., rotted, termite infested). Most everything else is generally easily replaceable. It looks like T1-11 siding, which is easy stuff to knock out and replace if chewed up, and its not terribly expensive. Replacing the doors - heck, just use a few pieces of that T1-11 and make doors out of it. The shingles look to be close to the end of their life - You could replace those (and replace any sheathing underneath) without much effort), then go either with shingles, a metal/plastic roof, or even roll roofing (although that doesn't necessarily looks terribly attractive, it'll work). Either way, this looks like a great project shed. If it were me - if that giant evergreen wasn't hugged up next to it, I'd be dreaming of putting solar on it, getting some batteries, and putting power to it!

Should be perfectly fine to use - but I would recommend the foam that has the critter-repellent in the mix to keep the critters from making foam Habi-trails behind the drywall and through the foam.

I've done a few things with spare fans - you can use pretty much any power supply that puts out 9-12V and you'll get good airflow - and yeah - like you and a lot of other posts are thinking, you'll want to make sure it puts out good current.
On my larger boxes where I'm using fans and TEC's, I use an old tower power control - even the relatively dinky ones are 350w and will drive your fans no problem with room to expand. You can get them new for 25 bucks and up. What I like about them is you have a switch on them - gives you control of whether the fans are running or not.

Glad you liked it! Started doing the 'sock technique' a few decades ago, and I'm at the point now where its my go-to, especially on woods that take stain up a little differently in patches. Not having brushes to clean up is a huge plus, too!

I've found the sock works even better. You can wiggle it around to expose less-coated areas, curl your fingers down and expose more area closer to the top of the sock to absorb/spread more stain, and getting the sock off of the nitrile is easier. Plus old socks are free! The reason I specified nitrile instead of latex for the base glove is to help resist the stain. Latex will start to allow some stains to bleed through. I use 5 mil nitriles, and they're great.

That is definitely a joint that's under flexing stress; anything other than a brazing or welding repair will not last. If you can free up that part so its available, a weld repair on that is maybe a 10-15 minute job (especially if you don't mind it not looking perfect!).

If the new P-trap is plastic, you don't need putty, and absolutely don't use pvc cement unless you want to replace it every time you need to clean the trap!
The seals should be fine. The only place you should be concerned is where it transitions into the main waste. The transition fitting should be cemented to the waste pipe, with the proper seals there. If its a metal nut to a metal transition, make sure its clean and the seal is positive on that pipe (that's the only place I've ever used putty - transitioning a new pvc p trap to an ancient pipe on a house built in the 1930's)

Be careful about over-sanding that veneer. I would sand enough to get through the sealer. And if it were me I would use a pre-stain conditioner to try to help even the stain application. My favorite stain applicator for something like this is a regular cotton sock put over a nitrile glove - that way I can spread the stain with better control, run over spots that I may be having some trouble with, and help remove any excess applied stain with the back of my hand.

The best attempt on a repair would be to pick away any loose bits of particle board that prevent perfect mating, then lightly coat both the chipped pieces and the base with a good quality wood glue and mate them together. Wipe off any excess you see when you mate them together, and clamp down on them using a piece of scrap wood to ensure they would stay in place. If it were me, I'd probably use painters tape to ensure they remain in place before I clamped the wood down. Regarding particle board, it doesn't look any dryer than your typical press-wood furniture; the wood glue will do a good job of forming a good bond.
Like the other post says, you might need to get a little creative with the bolts; my bet given how this looks, you might need to secure the bolts and such with some JB Weld on top of doing the repair, joining both the bolts and whatever flanges that those are secured to.

I have faced several of these types of transitions. If you have some of the original flooring, you could try to meticulously trim/fit a plank and shim it to the level of the floor then secure it down with construction adhesive, but I've found trying to make it "invisible" is difficult, and matching the gap, with its imperfections, is a meticulous process.
Next best (if you're good at matching staining and mid-level woodworking) is to take a plank and cut it into a threshold that fits relatively tight to that gap with some overhang onto the flooring, stain/varnish, then secure it in place. Finally, you can look for a store-bought transition that would do the same function as a custom built one - it'll likely not match as well, but it would certainly fill the gap.

As the other poster mentioned - you can definitely make the scratches far less noticeable on stainless. One of the products that I can recommend is something called "Rejuvenate". Its a metal polish paste that you can use along the grain of the stainless that works very well for minor scratches like what yours looks like.

For something that size, I'd probably just be patient with a dremel , cutoff wheels and a bunch of patience - especially if I'm trying to get as many rings out of it as I can. No form would be needed to hold it; you could mark the height you're cutting off on the tube and hold it with either vice grips or a good glove (it will get hot).

Do you know relatively where the lines run and the splices are? If you have a high degree of confidence, you could leave the water pressurized for a few days, then try driving a steel pipe down near the splices to see if you can locate a soggy patch of sub-surface dirt - kind of like attempting to take core samples of soil. Obviously you want to make sure you don't inadvertently punch a hole in your electric or damage the line further - hence the need to know where the line is!

You can use joint compound over thinset to restore a smooth surface, no problem. How I've fixed a problem like that is by loading a 12" plastic taping knife with joint compound, and spread a very thin coat over the thinset. I then let it dry, hit it with some drywall sandpaper to get rid of the ridges, then repeated with another coat that I smoothed with a drywall sponge. I recommend a couple coats of PVA primer on the fix prior to paint, just to ensure the paint gets a consistent bite (and you can see any spot repairs you need to do).

Had similar. The repair is actually fairly easy if you're relatively patient. Square off the hole to eliminate the jagged parts. Take a quick measurement from the lathe to the outer edge of the plaster still there - it looks like its > 1/2" inch so I'll base my next steps on that: Like previous posts have said, get yourself some 1/2" drywall - looks like you might make do with a half-sheet (4x4'), plus get a couple of packs of wood shims, 1 1/4" drywall screws. fiberglass mesh adhesive-backed drywall tape and joint compound (plus a pack of the plastic drywall taping knives if you don't have any). Cut the replacement drywall to roughly match the squared off opening. Then, use the shims in pairs perpendicular to the direction of the lathe to shim out the replacement drywall to shim up the drywall patch to the existing surface of the wall - screw the shims to the lathe with drywall screws and make marks at the top and bottom so you know where the paired-up shims are located. Put the drywall in place and screw the drywall to the shims. Tape the gaps between the repair and existing wall, and finish up the gaps with the joint compound, feathering the compound out onto the wall and repair board to minimize any waviness. Prime and paint.
Sounds like lots of steps but definitely one of the quickest ways to get a relatively smooth repair with a minimum of heartache.

If it were a newer GFCI then I'd start suggesting troubleshooting. If its anything older than 5 years and an outdoor GFCI, I strongly recommend replacing it as a matter of course, because they do have a finite lifespan and that lifespan is shortened with exposure.

Lot of good advice - I agree with the foam board, then wall, but the one thing I would do prior to putting the foam board up is to seal any cracks on the concrete wall with hydraulic cement then put a couple of good coats of drylok paint to help seal the wall. You've never had water in the basement, but you don't want to find out you have an issue behind your framed out wall and foam. - where you'll likely find the first sign of a problem is a large patch of mold.
If you're leaving part of the basement unfinished, I'd also recommend keeping a dehumidifier going in that space to help keep the humidity level at a consistently low-to-moderate level.

If this is to be painted, what would stop you from using simple router bits and replicate the shape on thinner stock, then face-glue the whole thing together? Seems a bit easier to break the shape down to simpler curves than trying to replicate the whole thing. The biggest pain is to have enough clamps to secure the whole thing together, but that does give you a reason to buy a bunch of nice new clamps (and considering they're useful in metalworking as well, that's not so bad!).