[RPG] Can the Telekinesis spell be used to manipulate liquids

No. The authors are careful about denoting when spells can be used for an attack.

There is nothing in the game rules more important than the action economy. Over and over again, the authors painstakingly indicate how spells and powers fit into the structure of "attack actions", "bonus actions", "movement", "dash", and so on. Given that there is no indication that telekinesis allows an "attack action" with the object, you can be assured that the authors meant there not to be.

There are times when the rules should be set aside in favor of "real" physics or dramatic license. However, the DM should set the bar quite high for this. The first question you should ask yourself should be, "Is my player asking for something that people like Jeremy Crawford and Mike Mearls didn't think of?" Rest assured, they thought of telekinesing a dagger across the room or a "dancing" sword. In fact, they designed spells that do as much. It is implausible that they did not consider the possibility and then failed to address it in the description.

Yes, based on the "fine control" statement

If we look at the examples that are given for "fine control," they could potentially involve holding things in place. For example, pouring out the contents of a vial would require holding the vial still (or still enough), and manipulating a simple tool could potentially require pushing the tool against a surface, holding it still. Additionally, there are no stated limits on that fine control, so there aren't any. After all, this is magic, not muscle power; our only limits are the ones explicitly delineated in the spell and the fundamental system restrictions.

Additionally, requiring that an object be in motion doesn't make sense. If you're trying to remove an item from a creature's grip, what happens if the two opposing forces cancel out and the item doesn't move?

Replicating Levitation is fine

You want to differentiate between levitation and telekinesis, but levitation is really just a subset of telekinesis. Note that telekinesis is a 5th level spell, but levitation is only 2nd level. Thus, it seems balanced to allow your player to replicate the effects of a lower level spell using a higher level spell.

There are many high level spells that could be used to duplicate lower level spells. Wish is the archetypical example, but the various resurrection spells and the "mass" spells also fall into this category.

Your player might be confused about the ring, and he might not use it to its full potential. Still, it makes more sense to make sure that he knows the full extent of telekinesis, rather than banning his preferred usage of that power.