> It is only the Senate which has the filibuster, and it merely exists as a Senate rule. It can be removed with a simple majority vote, though I believe rule changes must occur at the beginning of the new Congress.

Rule changes can occur any time, but except for the initial adoption of the rules by a majority vote by each House at the opening of each Congress are, themselves, subject to the rules adopted by that House for that Congress, which may impose additional process.

House can de facto filibuster in the sense that a 3 rep majority will inevitably lead to clashes internally, as every rep in the GOP absolutely will use this as an excuse to get concessions. This happened everytime this happens.

> It can be removed with a simple majority vote

It absolutely can, but both sides steer away from doing so due to situations like this - either party inevitably becomes the minority as some point in the Senate, so Senate leadership in both parties prefer to maintain it.

> That may be a moot point with regard to cabinet positions should the incoming Republican Senate go along with Trump's request for recess appointments, though

And that's my point. With Thune as Senate majority leader, Recess Appointments are basically moot.

The whole point of Recess Appointments is to undermine the power of the Senate, which much of the Senate obviously opposes.