Does DO-178C require static code analysis for level A software?
DO-178C is a means of compliance, so it sets out what you need to do to show you are meeting your required safety levels in your design.  It does not give advice on what methods you might use along the way.

I have seen static analysis used as part of the process, often with hardware integration and system testing.

DO-178 tools need to be qualified for DO-178 if you are using them to test your software.  I am not aware of anyone successfully using tools qualified for other standards (e.g. MISRA) in avionics.