Are these supposed to be a questions on what general methods would be used for each task?
(I have sometimes problem with these virtual experimental designs as homework questions, because sometimes they really lack the meaning behind a question, for example the question about cloning in real setting would need to include what would be the purpose of a clone, wha would anyone wanted to clone DNA and so on)
But in general, a) yes, you need
PCR/reverse transcription-
PCR but for the complete cloning also.. well the cloning itself which requires other basic methods

The first question is not clear for me, does it have two parts? Like the first - "what to use for cloning" and the second - "show genomic and cDNA" (sequence I presume), I don't really get what "show" means, does it mean how can you find yout the compltete sequence? There is a specific method that can tell you the sequence (after
PCR). From the practical point of view, the lenght of the protein and logically the corresponding DNA/cDNA has to be taken in account too (you can look up average weight of an amino acid to get idea how long your protein is and coding sequence will be). But as I say, that's the problem with these questions as I don't know how much detail is required (maximum detail is required in real life).
For d) EMSA can be used I guess, but there is one other general method coming to my mind first, that can tell you whether certain region(s) interacts with a specific protein, can you think of it? It's advantage is you can test more proteins and more regions at once.
e) I agree
As for b] Western blott will show you presence of a protein in a lysate and it's amount, specific antibodies can be used to detect phosphorylated form only (and I wonder what the question about this was left out as this is probably the first thing you would check, if it's phosphorylated), so your gene is a transcription factor, so you actually want to measure transcription of his targets, so....
You could detect the targets as proteins by WB, but do you think there is always an exact correlation between rate of transcription and amount of protein?
c) I have an idea fro this one, still having in mind the antibodies specific for a protein form.. and of course you need something to watch the cells in..