Although normally called an "adverb", probably is often used to modify an entire sentence - in which case it normally appears at the beginning (or the end, if it's "parenthetically" added after a comma)...
a: Probably I'll move to the south by then.
b: I'll move to the south by then[,] probably.
In other contexts, syntactically it's more like an adjective than an adverb, in that it normally modifies the immediately following term...
c: I'll move probably to the south by then.
d: I'll move to probably the south by then.
Both of these imply that you will have moved by then (possibly to the north, but most likely to the south).
e: I'll move to the south probably by then.
Implies that you will move to the south (possibly much later, but most likely "by then").
In their closest meanings, "still" is used for a situation that is ongoing or unchanged at any point in time, or regardless of any factor, stated or otherwise:
She still loves you. If you lose all your money, she will still love
you. Even when you were abusive, she still loved you.
"yet" has a similar interpretation, but describes the state of a something, within a process, at any given time within a progression, up to that point in a process:
He is yet a child. -or- He is a child yet.
He's still a child.
In another usage, it is closer to "already." In questions, it asks whether something has happened "already" or up to the time of questioning, and additionally implies that the addressee is expected or required to do it:
Have you called your mother yet?
Here the speaker possibly commanded or just expects the addressee call his mother, or was informed of the his intention to call his mother, and is questioning whether he has done it. "Already" doesn't have this force - it merely questions the completion of the action logistically:
Have you already called your mother? I wanted to say hello to her. (=Am I too late?)
Note that the idiom "have yet to" is used with the above meaning to express that something expected still hasn't been done:
He has yet to call his mother. (= He's supposed to do it, but hasn't done it.)
I have yet to see that movie. (= I've been meaning to see it, but haven't gotten around to it.)
"Not yet" - or "yet" in any negative context - is the opposite of "already:"
My father already sent me a birthday present.
My father hasn't sent me a birthday present yet.
Finally, "yet" can function as a conjunction like "but, however" that emphasizes a result obtained or a situation that arises despite certain factor(s):
He's only been speaking English for a year, yet he sounds just like an
American.
I've asked you a million times not to lock the door, yet every time I
come home, it's locked.
Note that "still" can replace "yet" here with the same meaning.
Best Answer
Both positions of "still" are acceptable, but after the verb ("He is still a boy") is much more common. (GloWbE has 86000 instances of "still + [be]" against 520000 instances of "[be] + still" (where by [be] I mean any part of the verb 'be' - am, is, are, were, being, etc.)
In Modern English, "yet" is almost confined to negative and interrogative contexts (it is a negative polarity item), so both of those sentences with 'yet' look old fashioned or poetical. I think the choice between them would be governed by prosody and rhythm rather than meaning.