I've been buying T-bills on TreasuryDirect for about 2 years. Let me answer your questions:
1. Yes it's reliable and your money is as safe as it can possibly be -- it's literally lent to the US government. The website looking like garbage is... unfortunately just how the government builds websites. Treasury.gov, IRS.gov, they're all bad. It works though.
2. You don't have to competitively bid. Select "noncompetitive" bidding which means you accept whatever rate the auction sets. This is what 99% of individual investors do. You specify the amount, pick the term (4-week, 8-week, 13-week, 17-week, 26-week, or 52-week), and submit.
3. Yes, you can set up auto-reinvest. When a T-bill matures, TreasuryDirect will automatically purchase a new one at the next auction. I have my 4-week T-bills on auto-reinvest and haven't had to touch it in months.
4. They issue a 1099-INT at tax time. T-bill interest is exempt from state/local tax which is a nice bonus if you live in a high-tax state. Only federal tax applies.
The Fidelity vs TreasuryDirect question is real though. Fidelity lets you buy T-bills at auction too, and the experience is much better. The main advantage of TreasuryDirect is you can buy I Bonds (only available there) and you're dealing directly with Treasury with no intermediary.