I frequently do English hymns as a prelude before the Requiem starts (i.e. the Subvenite for bearing the remains into the church proper). I have also done hymns after the In Paradisum... so those are other options to consider.

1. The Subvenite is not an entrance procession per se, so this requires some consideration. If the casket is already in place, there could be an processional in something other than Latin. The Subvenite, however, is part of the ceremony for greeting the remains and bearing them to its place in the nave... so I wouldn't use a hymn in its place if that takes place (my experience is that it is very rare for the remains to already be in place - which would imply that that ceremony for greeting the remains already took place some time before the Requiem was to start).
2. No.
3. No. The Libera Me is part of the ceremony of absolution, so you shouldn't replace this with a hymn.
4. In Paradisum is your best bet. It is, strictly speaking, not called for in the rubrics as the remains are carried out to the hearse - it is intended for the procession to the gravesite. Frequently, that doesn't happen much any more (i.e. an actual procession vs. driving). I can only think of one funeral in my experience where there was a procession from the church to the adjacent gravesite. IF there is singing at the gravesite (again, not necessarily common) - the In Paradisum could be done at the cemetery along with the Ego Sum and corresponding psalm / prayers that are part of the burial service as apart from the Mass.

Typically, I have the choir sing In Paradisum 2-4 times (depending on number of people accompanying the remains). In this situation, I might sing the In Paradisum once through (it is very short) and then transition to a hymn afterward.

I don't know if there were specific hymns requested, but here are several you may find useful...