Yes, interest rates going up lowers the price of bonds because "interest rates up" is mathematically equivalent to "bonds are cheaper."
The notion that changes in interest rates, which generally correlate with inflation, would alter the price of stocks is not obvious to me. Not sure what mechanism you would propose that would cause that to happen.
The US Government has the right to print USD. The notion that they could someday be unable to pay USD-denominated debts is therefore obviously wrong. Also, it is very much in the interests of exporters like China that USD remain strong, and they will likely just add the newly-minted USD to their USD reserves.
When proposing financial disasters, you can take these same types of fears and make them more plausible. E.g. propose that the US Government will overspend, weaken the dollar, cause the dollar to lose status as a reserve currency, and force future US debt to be denominated in something other than USD. Or propose that a sudden increase in inflation might cause effective salaries to decline or be uncertain, leading to a decline in consumer confidence and a recession.
Inflation uncertainty worries me the most. But I don't think there are any nightmare scenarios coming soon.