Yes, Trump is very cozy with Russia and Putin. It is clear that Russia interfered with the elections. Whether or not Trump was personally involved, it's evident that Russia interfered with U.S. elections to ensure a win for Trump, whom they will use as a puppet. In light of all this, impeachment is a possibility.
Only congress is capable of impeaching Trump, and with the extreme partisanship that has been occurring they will NOT impeach, and are completely willing to overlook any impeachable offenses.
Even if smoking gun evidence was found that he conspired with Putin himself to effect the election congress would only impeach under severe pressure from their own base. However since Trump is good at spinning a new worldview for his base the pressure will not be severe enough.
As Trump himself said; he could go and shoot somebody on national television, and he wouldn't lose any votes, or in this case be impeached.
We are currently a very long way from this point, but not so far to prevent speculation about whether Trump could be impeached. Were Trump’s team to be found to have conspired with the Kremlin to distort the 2016 presidential election, that would certainly fall into the impeachable category. But, again, it is entirely unsubstantiated. To take a flight of fancy, what if it were substantiated? That would again come down to a question of politics. No US president has ever been forced out of office by impeachment (Richard Nixon resigned before the vote; Andrew Johnson and Bill Clinton were acquitted by the Senate). Any such procedure would have to be prepared and approved by a majority of the House of Representatives, and then passed to the Senate for a two-thirds majority vote. As the Republicans hold the reins in both chambers, it would take an almighty severing of ties between Trump and his own party to even get close to such a place.
No, the new president will not face potential impeachment, however, he may face harassment for the FBI for any questionable actions and missteps that he has had in the past. The FBI does not have enough to impeach him or this would have already come out in teh recent election.
It is mind boggling how Donald Trump has gotten away with things that are worthy of impeachment. He will never be impeached. Politics will help prevent that. His candidacy is scandalous as well as his business dealings and very existence. I am completely disappointed that so many people in this country are allowing this circus to unfold.