the way people usually do it is by pulling down your protein of interest by either 1) using a specific antibody or 2) tagging your POE (with FLAG, GFP or HA) and pulling it using antibodies against the tag. Then, the samples are sent for Proteomics (MudPIT or similar) and analysis. This will find proteins that interact with your kinase, but not all necessarily will be substrates (they can also be activators of your kinase, inhibitors, substrates or scaffolds). Nevertheless, you will get some candidates.
The other option is using P32 and radioactive tracing of the fraction that's enriched in it after pulling down your protein. This will give you candidates that are phosphorylated by your protein.
The other option (although I'm not sure how this one would work) is knocking out your kinase and then do a pull down of proteins that are phospho-enriched (there are specific columns that do that), and compare it with your wild type sample. This will give you the proteins that directly and indirectly are phosphorylated by your protein. It would also give you the residues that get phosphorylated by mass spec.
Their is no easy way to answer your question 1) You can either try with the chemical genetics strategy or 2) Do a complete phosphoproteome analysis for your sample of interest and then use bioinformatics to predict the interactions.