Trying to break down 2 sentences (Genki lesson 15 dialogue 1)

Question

Going through Genki and Lesson 15 has brought up 2 grammar points I can't figure really out.It would help me a lot if I understand how those two sentences are build up and why they need those parts.

道子さんがquotationと言ってたから。

to itte :said takara I think I have to break it up as ta and kara. ta being casual for desu.. But i don't get why it would need the copula. so the question is what is "ta" doing there? The translation would be Michiko told me to invite you. (the quotation is たけしくんも誘って)

みちこさんのうちに行こうと思ってるんだけど、一緒にいかない 。　 ikou= volitional casual form of iku to omoutte= plan on doing. thinking about、 Here i have thought of several things sort of thing the "ru" is an abbreviation of iru n is added as it is an explanation. (I see it as connected with the proposal that follows of isshouni ikanai. and I think iru no could have been used as well. da as the copula kedo : is making the connection with the suggestion that follows. 一緒にいかない the translation according to Genki. I am thinking of going to Michiko's home. Do you want to go?

But again I am really unsure what the da is doing there.

Thank you for your time.

Answer 1

道子さんがquotationと言ってたから。

This た is not the copula. 言ってた is a contraction of 言っていた. Where ていた is the past (perfect) form of ている indicating continuation of state. By the way た is never the copula. It would always be だ.

みちこさんのうちに行こうと思ってるんだけど、一緒にいかない

In this sentence you've already figured out that てる is a contraction of ている (strange how you missed it in the first sentence), and that ん is a contraction of の. So in full it would be 思っているのだけど.

This ん/の is the explanatory の and it sounds like you already understand how this works in this sentence, so I'm a bit puzzled as to why you have problems with だ. The copula in some form: です, だ etc. normally (always?) comes after the explanatory の. That's a grammar rule. Just saying 思ってるんけど would be ungrammatical. After all, 思ってるんだ roughly translates to "it is that I'm thinking", so adding だ seems like a natural thing to do.