Pronoun "tą" is correct in Instrumental case ( Rozmawiam z tą kobietą - I talk to this woman). In accusative case, the correct form is "tę" (Widzę tę kobietę - I can see this woman) - but "tą" is accepted in quick or colloquial speech, while it is not really correct. So, in Accusative, the form tę should be used in neat speaking or in writing. Here is an article on that subject, and here another one.
No. Polish "tamten/tamta/tamto" is only English "that", while English "that" can be either Polish "ten/ta/to" or "tamten/tamta/tamto".
Read more here: "Why English "that" is sometimes Polish ten, sometimes tamten?"
You need to use "that".
Polish "tamten/tamta/tamto" is always English "that". But English "that" may be either Polish "tamten/tamta/tamto" or Polish "ten/ta/to". I know that this is weird, but you may read an explanation here https://forum.duolingo.com/comment/26090156 .
You could also read that https://www.clozemaster.com/blog/polish-demonstrative-pronouns/