Define:

the nominal rate convertible pthly

the effective annual rate

I assume that "interest at 5% compounded monthly" is american english for "a nominal interest rate of 5% convertible monthly"

The key thing to remember when converting effective rates to nominal rates is:

or, equivalently

or, in english

if the nomimal rate (convertible pthly) is x, then the effective pthly rate is x/p

Applying this to part 1:

The effective quarterly rate is supposed to be 6.6/4 = 1.65%

This is an annual effective rate of = 1.067651543

you want to find a monthly nominal rate that has the same annual effective rate

solve for .

can you finish from there? (part 2 requires no new concepts)