I'll try to only point relevant morpheme boundaries:
1. [[[kawaigat-te-i-ta Inu] ga shin-da] kodomo]
love-CONN-PROG-PRF dog NOM die-PRF child = [[[was-loved dog] died] child], "the child who loved the dog that died".
2. same.
3. [[[shinda Inu] wo kawaigat-te-i-ta] Kodomo]
die-PRF dog ACC love-CONN-PROG-PRF child = [[[died dog] was loved] child] "the child who loved the dog that died".
4. same as 1. -------------------– leoboiko 2 hours ago
(cont)
5. [[[[Chiizu wo kut-ta] Nezumi] wo tot-ta] Neko]
= cheese ACC eat-PRF rat ACC catch-PRF cat, "the cat that caught the rat that ate the cheese".
6. [tot-ta [Nezumi ga chiizu wo kut-ta] Neko] = catch-PRF rat NOM cheese ACC eat-PRF cat
= [[caught [rat cheese ate]] cat]?
(wow, I didn't know this structure). OP, feel free to fix/copy these glosses into the answer. – leoboiko 2 hours ago