How can I write regular expressions(REs) for any language that are syntactically correct.

For example, Turkish has two classes of vowels — front and back. Vowel harmony states that words may not contain both front and back vowels. Therefore, most grammatical suffixes come in front and back forms, e.g. Türkiye'de "in Turkey" but kapıda "at the door".
front = { a, ı, o, u }
back = { e, i, ö, ü }

And how can I draw a Finite Automato for these REs

Can anyone give me simple examples.
I will try to write regular expression for the whole grammar of language and than write the code in C. But need some starting point.

Why would you need regex. I can think of a way to do that without it.

I supposed to do so.

Write one with three states: one for where it hasn't seen any vowels yet, one for where it's seen front vowels, and one for where it's seen back vowels. And a failure state if it has to be a deterministic FA. I'll leave the edges to you.