Well "feel" in professional letters is not so recommended ! It is not grammatically wrong though ! He has to decide upon objective assessment not feelings ( experiencing of emotions and sensations ) ,when hiring someone .( It should be so at least :) ) You better us 'decide' for example among other possible choices. Because a decision is a resolution in the mind as a result of consideration . So you hope he considers your application and decides you are suitable as a consequence .

I really think that's correct. You hope that his opinion about you, will be ... ... To have an opinion about someone/something is exactely one of the meanings of "to feel".

That is valid, yes. I have written the same thing myself I am sure. :-)