I've seen something like that recently (not necessarily made recently), but it was a TV series which had an episode like that (not a movie). Most likely a police-procedural type, as that's been my staple of late. Possibly one of the CSI franchise, possibly "Lucifer", or "Castle". If I recall correctly, the zero-g recoil of firing a gun caused a bruise on the back of the gunman, leading to the truth coming out.

And after a brief dive into "1990's supernatural TV shows", I think that the one with the cloth is "Mysterious Ways". Male and female protagonist: check; paranormal investigations: kind of (he seeks out miracles and wonders; round glasses: no.

My mind brought up "Burning Zone", but that was mostly about diseases, and the episode summaries on IMDB didn't seem to have one about a healing relic.

I remember the cloth having healing powers - but the age meant that it degraded. From memory, it ended up being about 2 inches square, and kept in a bowl of heavier-than-air noble gas (krypton?) to preserve it.

Does this have one of the faces from Mt Rushmore (or an equivalent) moving backward into the mountain, and becoming part of the giant (alien?), which needs to be defeated? Is one of the girls working on sculpting a face on the mountain? I don't remember the title, but I remember these things, and if it's the one you are thinking of, it might help someone else get the name. The one I am thinking of aired (in my region, at least) some time in the 1980's (maybe early 1990's), and was hand-drawn or cell-type animation, in 2D.

This is not really close enough to post as an answer, but there are elements of "Ender's Game" which almost match.

Only a comment, because it doesn't really match (but memories are funny like that). It's possible that you are remembering a scene from "The adventures of Baron Munchhausen", where the Baron encounters the king and queen of the moon. They can remove their heads, and often float about with just the head and the neck-ruffle collar. In one part, one of the bodies (separate from the head) is being tickled, and the head is laughing. The heads are not translucent, and I don't recall a cigar, though.

Entirely unsure, because if I have seen these films, it was more than 20 years ago, but could it be one of the "Mad Max" movies? Car chase, Australian wasteland (very desert-like). A gun mounted on one of the cars is in keeping with the theme, too. The first Mad Max was 1979, but a Google search will most likely bring up the more recent in the series (Mad Max: Fury Road from 2015)

What was the control mechanism? There was a Playstation 2 game using the Eye Toy (I think that's the name) camera, and the player actually moved to make the on-screen avatar move (that is, it didn't use the hand-held controller). I don't know the name of the game, however.

Just to note, the movie you name as "Number 5 Lives" ("Nummer 5 lebt!"?) was released as "Short Circuit" in the US (and some other English-speaking countries).