1)  Mueller's Independent investigation 'through' the FBI.

2)  Congressional Committee investigation.

Mueller will _not_ subpoena Trump "to appear before the committee."  The Committee has its own subpoenas, but the President and the executive branch can ignore them, because the Committee is legislative, and the branches of government are separate branches of government not accountable to each other, other than what is stipulated in the Constitution.  Pence has refused a congressional "invite."

Bill Clinton was obligated by law to testify under oath because of Paula Jones sexual harassment case, so yes I believe that Donald Trump would be obligated to testify, probably under oath.  Clinton btw did not get in trouble because he did not keep his pants on, but rather because he perjured himself under oath.  It is a very dangerous position for the President to be answering questions under oath from an independent investigation.  I don't know what would happen if he refused, he has said he would answer, but let's wait until we get to that bridge, before we try to cross it.

Trump and his lawyers would like the questions in advance, I do not know of any good reason for them to be presented that way by Mueller.

I imagine that if Trump refused to testify, or declines to appear, than it would become pretty clear that Donald Trump would be "obstructing justice," which is something he wants to avoid.

Bill Clinton lied to the independent investigation, was charged with perjury and was impeached by a (Republican) Senate.  I seem to remember he was not removed because the House had become Democrat at that point, although I am not sure about the details.  So, yes there are ramifications for lying to an FBI investigation.  But if the Senate stays Republican, they're probably not going to impeach a Republican President (even if it is Donald Trump).

I don't think the US Marshalls enter the picture anywhere.....

Trump has said that he will appear in front of Mueller, under oath, "if" his lawyers will let him.  I don't think that it will have to go to subpoena, that would imply that Mueller is compelling Trump to testify, and I think that would look bad, especially for the President.   Resisting too much would be bad for the President, who after all, likes to assert that there is nothing to look for.

One thing you should remember is that Trump's family is involved because of particular kind of feudal mentality.  if it was just him, he might be able to resist, but Jared Kushner is involved, and to a lesser extent Ivanka Trump too.  General Flint's son is involved, which is one reason why he is cooperating so much.  So I imagine that if Trump doesn't come off as his usual antagonistic self, Mueller will have a good reason not to look too closely at Kushner and Ivanka, and maybe others in his family.

But, if Trump refuses, then we may have a constitutional crisis.  Meaning that we will figure it out then.  But again, Trump's family (and business) is involved, and that may well be a massive vulnerability.  Opponents do not necessarily have to go after just him, he has invited them to go after his family but involving them in his administration.

But again, I think it is important to remember that there are two investigations, although I would say that the independent investigation FBI is more important than the Congressional one (although Trump could conceivably fire Mueller, he cannot do anything to stop the Congressional one).

US Marshalls are in the Justice Department, but not in the FBI.