Resolved questions
Korean sentence structure and to be verbs...?

So I've been studying vocabulary, mostly, but making sentences with the words I've learned has actually been confusing (Nooo!). I have a few questions on where to place words and if some are necessary to use at all.

First, when adding more than one verb to a sentence, where to place the verbals (participles, gerunds, infinitives)?
Ex. I wish to give you a piano.
You should watch the show I'm looking at.
Next, in sentence structure, how are compound sentences formed? Are all verbs in the sentence placed at the end like simple sentences or (independent clause) conjunction (independent clause)?
Ex. I jogged early in the morning and now I am relaxing on my couch.
If we continue searching, we can find the key and you can unlock the treasure chest.
Lastly, is it needed to add "-ah/"-yah" or is it superfluous (Is "Nan yeoja ya" or "Nan yeoja" better?)? Is it only needed in sentences describing things?
Ex. I am going to bed.
Why are you putting on gloves: is it cold outside?

Thanks! :) I love you guys!