Explaining the table in the scribblings. 

We have seen algorithms for various decision problems for regular 
languages. Exercise to reader is to remind yourself of how to do this (if 
needed).

We have not yet seen any proof that a problem is not decidable. All of 
that will be done later.

That leaves the two positive statements about context-free languages. We 
did mention these at some point. The acceptance problem is handled by 
converting the grammar/PDA to a grammar in Chomsky Normal Form. In such a 
grammar we can predetermine a limit on how many steps a derivation might 
take, and therefore the algorithm of "try all derivations of that many 
steps" works. The emptiness problem is a (nontrivial) exercise.