The trial is fully functional. What fonts do you use for other projects? They should work just fine with InDesign.
Thank you for your reply
below are the problematic letters.
I want to use fancy headers such as
yet did not work
The applications you are using have no bearing on what glyphs are included in any particular font. If the font vendor includes the glyphs you need, then the font will work in ay application, if they do not include the required glyphs the font is not going to work for Turkish at all.
Your most likely choices for fonts that support Turkish are OpenType fonts designated as "pro" or "com"
This means very limited font alternatives.
Depending on what you have installed on your system, there are quite a few fonts that carry those glyphs. An ease way to check is to copy the glyphs into a text frame, select them, put your cursor and click on the font name and then click the down arrow on your keyboard. This will show these glyphs (or lack thereof) of each font you have on your system one at a time. You'll be able to see which fonts have them and which don't.
And in InDesign CC you can mark them as favorites.
I already did so yet found just 2 fonts
Are you on Mac or Windows?
On my Windows 8.1 I'm only through fonts starting with letter "C" and have counted already 20 fonts that have those glyphs.
Same thing on a Mac Yosemite. Granted I have installed some Typekit fonts but as a Creative Cloud Subscriber you have access to those fonts too.