1 - Does one have to always change the language direction of a TM file, when translating with OmegaT? In other words, should one transform an EN-TR *.tmx file into a TR-EN *.tmx file in order to use it when translating a document from Turkish to English?
There's no need to change the direction of a TMX in OmegaT: OmegaT automatically picks the translations in the right direction.
That doesn't mean a project works both ways, but a TMX created by a project can be used in another project in the reverse direction.
2 - I'd like to ask the same question regarding the usage of glossary files: does one have to change the language direction of a glossary file (for example, EN-TR) into the other direction (in this example, TR-EN) when translation in the opposite direction?
Text file glossaries have to be reversed manually (generally in a spreadsheet) by switching the first and second column. TBX glossaries are read both ways automatically.