Glad you could get it to work again! Nothing like a good deadline to encounter such problems.
Here is a bit of background information:
A font consists of 'regular' characters (which you can type in from a keyboard; those are indeed Unicode characters), 'special' characters (ligatures, Real Small Caps, Oldstyle numbering, etc., which typically are not valid Unicode characters), and a list of commands which say "if these two character go in, replace them by this single other one instead". That list of commands specifies OpenType ligatures -- and it doesn't really work on characters, but on glyphs instead. A 'character' has a Unicode value, but a 'glyph' may not have one -- it's just an index in the list of all individual drawings in the font, specifying the nth glyph in there.
When all's well, this is not something you'd ordinarily notice. InDesign keeps a list of all fonts, and of all characters and glyphs in all of these fonts, and its OpenType Glyph relations (which, as you may deduce, are only valid for the font they appear in -- some fonts have more "glyphs" than others, and the Glyph Order varies wildly from one font to another, as you can see in the Glyphs Panel when sorted on "GID" (= "Glyph ID")).
What happened with your system is that presumably InDesign got the list of 'glyphs' from one file, but OpenType features from another file, with the exact same font name! So the perfectly normal operation "if you see glyph number 15 followed by glyph number 31, replace it with glyph number 65", meaning for that one font "replace "f" followed by "i" with the glyph "ﬁ"", got confused and instead came to mean "replace "i" followed by "l" with "Š"" (its proper name is "S Caron", with the Caron being this V accent).
So possibly you had more than one version of the same full font name installed (not the file name, but the internal full font name; "Times New Roman Italic", for example). One of the tricks to check this is to select this weirded-up text and disable Automatic Ligatures. If you see it revert to readable text, then this was the issue.
It's also possible something inside your system got confused -- InDesign, written by Adobe, accessed loads and loads of Extra Tricks in fonts that your typical other software doesn't care, or even know, about. That's why mishaps of this kind are typically picked up first by InDesign.
The Find Font dialog is your friend in tackling this issue. You can inspect the file paths of the troublesome fonts, and see if there is anything out of order; for example, you might suddenly see an unexpected file path. A tell-tale sign of Double Font Syndrome is when you physically remove that font file out of InDesign's view, and you can still see it works in InDesign -- but now with another file path in the Find Font dialog. At that point you only have to decide which one of the two was the "correct" font file ...
I have a similar problem and I tried the solution you suggested to check if the problem is with the Ligatures. However, when I disable the Ligatures, the text does not show readable again. What can I do ?
Thank you in advance!
I have resolved the issue.
can you tell how you resolved the issue?