A: If your parents are outside of the US, the whole process should take about a year (maybe more, depending on COVID delays) before they are able to come to the US.
If you are petitioning them while they are already in the US, it will take about 6-10 months to receive their green cards.
As the other answers have mentioned, it's no problem at all for you to move during the process, as long as you change your address with USCIS every time you move. That way you won't miss any notices from them.
A: A B2 visa rejection would not normally affect the H4 eligibility, but it depends why the B2 was rejected. If you're concerned, I would recommend that your wife speak to an attorney in person before applying, just to make sure there aren't any issues that would prevent her from qualifying.
A: You can look up Form I-864 Affidavit of Support and read the instructions to find out what it means to become the financial sponsor for an intending immigrant. Basically it is a contract with the government stating that you can support the immigrant and will not allow them to become a "public charge" (like go on welfare or food stamps, for example).
As for the money you may have coming in a few years, you should speak to a wills and estates attorney in your area. There are probably ways for you to protect this money but that will depend on state law where you live.