Question

"This is my old book " name the pronoun and its type in this sentence

Answer 1

Because the first instance means “THIS IS my book” and it is a finished sentence, when the next instance means “THIS book of mine” and it is just a phrase, not a sentence. You are technically correct with all the agreements with gender, but meaning here is different, that is why you are confusing two separate things.

эти мои книги is correct for plural in a descriptive nature of things as a phrase, but if you want to state the fact that these PARTICULAR books ARE yours, then you could use это in front as POINTING at them, which will make it a sentence of its own. In both instances with это there is IMPLIED “IS” or “ARE”, which is understood and completes the sentence. With examples with эта and эти there is NO implied VERB, which only limits to these statements being phrases and not sentences.

Answer 2

Because the first instance means “THIS IS my book” and it is a finished sentence, when the next instance means “THIS book of mine” and it is just a phrase, not a sentence. You are technically correct with all the agreements with gender, but meaning here is different, that is why you are confusing two separate things.

эти мои книги is correct for plural in a descriptive nature of things as a phrase, but if you want to state the fact that these PARTICULAR books ARE yours, then you could use это in front as POINTING at them, which will make it a sentence of its own. In both instances with это there is IMPLIED “IS” or “ARE”, which is understood and completes the sentence. With examples with эта and эти there is NO implied VERB, which only limits to these statements being phrases and not sentences.

I don’t know if I am making sense to you with my attempt to explain ;) I am a native speaker or Russian and it is intuitive to us, more than based on rules. We study these rules at school, but I have forgotten how to properly explain it. I think what is happening here is that you are confusing different parts of speech ( ex: adjective, noun, verb etc.). They sounds the same, but they are used differently in building a sentence.

Please, forgive me, if my explanation is not what you expected.