Regarding 1., I don't know how much this applies to US, but make sure your other bank is not owned by a first bank in which you have account, or if they both are not owned by the same entity.
https://www.fdic.gov/resources/deposit-insurance/brochures/d...
IntraFi Network Deposits, which is number 5 on the list, has 3000+ members, so there for sure number options even if directly managing the risks.