First of all, it's for
Eseeable.
It's just like the "fore" in before (since you are "foreseeing" it -- before it comes into existance).
Typically when we use "foreseeable future" it's to express some sort of planning.
Your first sentence doesn't work at all -- I don't really know what you're getting at with it?
The second one technically works, but it doesn't sound natural -- a bit wooden to my ears. I would say something more like "I won't have any free time (or maybe "open appointments," "free days," etc. -- whatever is appropriate) for the foreseeable future."
The third one also sounds weird to me. Again, I think it's technically right, but it doesn't sound natural. I would just say "I'll be around for the next week," or "I won't see you again in the foreseeable future."
A couple more random examples:
"The company's board of directors doesn't expect to make any further acquisitions in the foreseeable future."
"For the foreseeable future, I don't anticipate on purchasing a new vehicle."