I normally use an additional piece of downspout and connect it to the elbow at the bottom of the downspout. They come in 10' lengths and in several colors. I just cut them to the length that seems like it is long enough to do the job. Use sheet metal screws to hold it together. Make sure that you have it extended beyond any landscape edging that may trap water in a planting bed next to the foundation.

I would just replace the fill valve. Takes maybe 10 minutes and costs about $8. If I'm doing that, I would replace the supply line from the shutoff valve if it is a flex line. They have a somewhat limited lifespan and can be a big deal if they fail.

It will really depend on your individual situation. Your plan will certainly help, but no way of knowing your exact situation. Are you getting water in the basement now? One common overlooked solution is making sure your downspouts are long enough to carry water away from your foundation and are flowing downhill away, not allowing water to flow back to your foundation.