Sit v. sit down

I seriously cannot find any good, thorough responses to this question, and I'm trying to help out a non-native friend.

Sit down implies motion. I understand that because of the preposition "down". Sit, too, can imply motion. The only difference I can find between the two is when you try to make "sit" transitive, it simply doesn't work. "He sat me DOWN" "he **sat me".

That being said. All of the following sentences (for me) are correct: "please sit"/"please sit down"; "why are you sitting?"/"why are you sitting down?"; "I can't reach this sitting"/"I can't reach this sitting down"… That last one could sound a little off just because it sounds like you are trying to reach a sitting of food or something, but that's about it. In all verbal tenses I still understand the two of them the same way. So is the only difference between "sit" and "sit down" the fact that "sit down" can be transitive and "sit" not?

If someone could give a more detailed response about the differences between the two, I'd appreciate it. I don't want to give a flimsy response to my friend.

First of all, "sit" is not transitive. "Set" is transitive. I would consider "He sat me down" an irregular construction. "Sit" can, however, be reflexive—"I sat myself down". As to the issue of redundancy raised by ViruZX, the somewhat redundant "sit down" is often used intentionally in command form, as an intensifier. You hear the same type of redundancy-for-effect in "Come back here right now!" (or in the extreme case, if Mom is quite angry: "Throw that thing away, march yourself back here upstairs—right now this instant—and sit yourself down, James Henry Jefferson!" Now, that kid knows he's in big trouble.

Contrarily, it might be that people say "sit down", calmly, to be polite, because "sit" is what you say to a dog. More polite is the formal, but quaint: "Please be seated".

Oh, by the way, you can say "We all sat down to dinner." but you would not say "We all sat to dinner."

I recall a teacher talked about this while we were discussion poor language usage.

What is the difference between "Advance" and "Advance forth".

There is none apart that in "Advance forth" you are saying the same thing twice. Advance already implies that you go forward.

The teacher said that the one saying the same thing twice is not very grammatical but still accepted.

Here we have the same situation only replace "Advance" with "Sit" and "Forth" with "Down"

Even if it sounds like it doesn't work - it does.