Sounds like an older model. May be time to replace then. It’s definitely not clogged or anything like that. If so you would have pressure problems when turning on the hot water. If you can’t afford a new one, watch a video on how to clean the sediment tank and attempt that, I should caution you that doing this on a gas system is risky if you are not well versed in this area.

Well the good ones have a life expectancy of about 8-12 years. My last gas water heater lasted right at 9 years before I had to replace.

Not for this. A simple push of the button should do. I have restarted and relit my pilot light without draining the tank with no problems. How old is the water heater?

There are usually reset buttons on gas water heaters for the thermostat. The reset button is often red and located near the thermostat or behind a metal panel that is removable on the unit. When you find it, push the reset button and then release it. There may be a lower thermostat button also known as a second reset button.

Well in that case it may be worth the split unit nuke brought up, however those can get pricy if you do not know how to install yourself. The unit may be reasonable, but labor is usually expensive. I had one put in a room I built inside a non climate controlled warehouse and it was about 6k. The one I put in was larger than the one nuke shared earlier.

This should not be an issue either. Just like nukethemoon said below you can utilize a dehumidifier with a fan if you are overly worried about air quality/air flow. What are you using the basement for? If just for storage I would not do any of this and save my money.

Vents are not necessary in a basement. Places that are underground tend to stay cooler naturally. Only way I would do this is if someone was going to stay down there permanently or I was going to use as an additional room.