There is an almost direct correlation between CD rates and the risk a lending institution takes on. Virtually all of the lenders that offer the highest CD rates are taking on the greatest risk on the asset side of their balance sheets and are thus at higher risk of failure. That’s how it works. As a depositor you take on greater risk to get at that greater return. The only exceptions to this are that some banks run short-term specials (to drum up business) and credit unions often pay higher CD rates because they pay no corporate taxes and this allows them to subsidize their depositors (and borrowers, for that matter).
IndyMac is a high-risk lender, although not as high risk at the moment as Countrywide and Accredited, for example.
If an institution fails and the FDIC takes over, your total deposit relationship (that is, the sum of your savings, checking, CDs, etc.) is covered up to $100K. Anything above $100K is subject to loss. Joint and other accounts are considered separate for insurance purposes.