How to add a dot above character ?

It’s very easy if you have a sharp pencil or a good pen.
Just kidding! :-)
This might help: https://creativepro.com/finding-and-changing-glyphs.php
(That assumes that there is such a character in your font… an omega with a dot over it)

According to this post elsewhere
https://forum.openoffice.org/en/forum/viewtopic.php?f=7&t=48069
you’ll need U+03C9 GREEK SMALL LETTER OMEGA, followed by U+0307 COMBINING DOT ABOVE
and a font that supports “combining dot above”

Works for me with Lucida Grande, Helvetica Neue (on OS X 10.9)

Still works for me with GREEK CAPITAL LETTER OMEGA U+03A9, followed by the combining dot.

For clarity, the capital omega looks like the one used for a logo by the watch company, and the small omega looks a bit like a curly W.

Aha, problem: I was trying it out in TextEdit, but in InDesign, the dot crashes into the character, isn’t high enough to avoid the top of the capital omega… hmm.

Workaround:
use Character Viewer to insert the capital omega,
click baseline shift (about 3 pt depending on font size),
go back to Character Viewer to insert the combining dot above,
pick a font that displays it OK.

Maybe.

Chris.

Edit after seeing your edited reply: almost as terrible as the solution for the Welsh W+circumflex, when a client insisted that we had to use a font that didn’t contain that letter. We had to insert a floating circumflex and use insane amounts of kerning to float it into position (different amounts for different font sizes), then copy-paste every instance!

Wow, using an Illustrator EPS is a sad solution. Ouch.

This script would have helped: https://creativepro.com/easy-diacritics-and-other-tough-glyphs.php

Once you have one of them, you could probably copy it and then use find/change to replace the others… see tip #5 here: https://creativepro.com/10-findchange-tips.php