If b is not necessarily equal to c, this is just an elementwise inequality, which can be entered as [a b;c d] >= 0` or perhaps a small positive number such as 1e-5 instead of zero. CVX treats all inequalities as non-strict.
If this is meant to be symmetric matrix and a semidefinite constraint, follow the guidance at Semidefinite programming mode — CVX Users' Guide . .
As for the 2nd question, you haven’t shown how the expression will be used. Look up linear-fractional at Convex Optimization – Boyd and Vandenberghe .
And the first thing to do is to read the entire CVX User’s Guide, as well as