Solution

1. The family of context free languages is closed under homomorphism: TRUE
   Example: Let L = {aⁿbⁿ | n >= 1}, h(a) = 01 and h(b) = 111.
   => CFL for L: A --> aAb | ab
   => CFG for h(L): A --> 01A111 | 01111
   Hence, h(L) is context free language.
    
2. The family of context free languages is closed under reversal: TRUE
   Example: Let L = {anbn | n >= 1} is context free language.
   => CFG of L: S --> aSb | ab
   => By reversing the right hand side of every production, the reversal grammar can be obtained.
   => CFG of L^R: S --> bSa | ba
   => L^R = {bⁿaⁿ | n >= 1} is context free language.
   => Hence, context free languages are closed under reversal operation.