Can the republicans do what they believe the democrats are doing and impeach Joe Biden?

Not unless they have a valid reason to do so

They can try, of course, but they'd have to cite the specific cause.  When Andrew Johnson was impeached, one of the charges was because he made a bunch of speeches where he lambasted members of Congress and ridiculed them.  Basically, he was impeached for making fun of them.  Hardly what anybody would consider to be a High Crime or Misdemeanor, but there you have it.

Marjorie Green can spend her time drafting articles of impeachment against Biden, or Obama, or anyone else she wants to attack, but the process for getting those articles heard is long and requires some kind of political inroads, which she no longer really has (at least she won't have those avenues for the next 2 years).  She would be doing a better job if she spent the next 2 years pushing for Congress to adopt measures that more strictly lay out rules for how impeachments should proceed, how much power the President should have, when judicial appointments can be heard, etc...  Trying to go after Biden with such a dramatic stunt just makes her into a tool that can be manipulated, and it shows just how little power she really has to wield.

She’s wasting her time and everyone else’s time. She’s an idiot who’s trying to make a name for herself so she’ll stay relevant. 

She can draw up all the impeachments that she wants but for the next 2 years, it’s going nowhere.  Have you forgotten that the Democrats control the house. Only the house can vote to impeach or not. Good luck getting enough democrats to agree to impeach Biden. Why would they impeach Biden when the republicans refuse to convict trump the first time. 

That would be a threat to National Security, and would not be allowed