Don't forget about vowel harmony - aka a and ä cannot be in the same word -> tässä :)
Without a noun, 'tässä' and 'tuossa' express the place of something, but here we are using 'tämä' -> 'tässä' as a demonstrative pronoun. Demonstrative pronouns take the same case as the noun too, that's why it's tässä metsässä and not tämä metsässä. Latter means "this in the forest", but here we want to say "in this forest" instead.
Yes, actually the front vowels (ä, ö and y) don't go together with the back vowels (a, o and u). Middle vowels (e and i) can exist with both groups but usually words with only e's and i's will also use ä in cases.
Only times these vowel groups exist in the same words are when a word is a) a compound word when it consists of two different words and there is a small pause between the words which makes it easier to pronounce and b) in certain loanwords and with them you can hear how Finns struggle with pronouncing the correct vowels because it lacks the vowel harmony. (E.g. "olympialaiset" easily becomes "ölympialaiset" or "olumpialaiset"!)