Hi everyone!

I hope this is the right forum to post my concern in.. I took an acceptance test for a tourism school in Austria today. It was mostly a multiple choice English test ( a pretty hard one). I was not sure about a few things.. Maybe you could help me:

"He is being very annoying." - Is that proper English? During my time in the US I heard a lot of people say that.. But is it grammatically correct? Or can you just say "He is very annoying"?

"Recently I came across a great book.." - This sentence was in a text in which we had to find errors. I thought because of "recently" I would have to use present perfect. So I changed the sentence to "I have recently come across a great book" (he then tells about the book). Is that correct?

"I have appreciated his help and support" - Can I say it like that? It sounded a bit odd to me. Shouldn't it be "I appreciate his help and support" because it is a state?


I knoe this is a bit confusing but I would really appreciate someone's help with this!
Thanks in advance!!
simone