I don't think the first one sounds like you're treating someone like an object any more than saying, "I want a girlfriend," in English does.
In your second sentence, are you saying you want to study many Japanese things or that you want to study Japanese things a lot? The way you're using たくさん is modifying 勉強, if you want to say "many Japanese things", たくさんの日本のこと is the way to go. Also, I'm not sure I would have gone with 勉強 here myself. To me it sounds odd that you want a Japanese friend to "study" Japanese things. Though one of the native speakers on the board could better tell you if that sounds alright contextually. I probably would have gone with something like, たくさんの日本のことについて習いたいですから。
As for number three...I'm not entirely sure what you're saying here aside from your first sentence. Though that could just be me; I definitely need to practice more myself.
時間は買えない大切なのだし
I honestly have no idea what this is supposed to mean. "Time can't buy important things"? Is the の supposed to be もの or is it standing in for another noun? I'm not sure if the context is clear enough to have の performing its stand-in role here. Or is it casual んです? If it's supposed to mean what I said, then the sentence would be better constructed as: 時間は大切なこと(もの if you're only talking about physical things)を買えないし
一度過ぎたら二度と絶対帰って来ないだ し
"If (something) passes, then you will definitely never be able to return"? So if you let something pass you by, then you may never get the chance at it again? I really don't know, hopefully someone else will try to help with this one. Though 絶対 needs to be 絶対に to be an adverb.
As for the difference between 休み and 休日, 休日 is more polite/formal. Like how 本日 is the more polite/formal version of 今日.