Answer: Before I answer your specific questions, let's make one point very clear here. Prepaid debit cards will not help you build credit. I don't care what the brother-in-law of your best friend's nephew or even Suze Orman tries to tell you, there's no way to improve your credit scores through the use of a prepaid debit card. That's a fact.
Now that we've cleared up that confusion, let's move on to your questions. If you're unable to open a free checking account at a bank and you simply want a card that will act as a substitute for a checking account, a prepaid debit card might be the right choice for you. A credit check shouldn't be run as part of the application, and you should have no problem getting approved. You won't be building credit, but at least you'll be able to enjoy the convenience of shopping online and carrying plastic instead of a wad of cash in your wallet.
My concern is your questions seem to stem from the overall desire to purchase a home in the near future. If that's the ultimate goal, then a prepaid debit card isn't going to remotely move you in the right direction. So take a pass on the prepaid debit card, and consider focusing your efforts on the responsible use of a secured credit card instead. Unlike prepaid debit cards, your payment history for secured credit cards will be reported to the credit reporting agencies, which means your credit scores can benefit from its use.
In addition, after responsibly using a secured card for 6-12 months, your FICO scores may even improve to the point where you can get approved for a regular unsecured credit card or perhaps a mortgage with reasonable terms and rates. Just remember to be patient because it will take time and dedication to get your credit back on track, but your efforts will certainly be well worth it!