Is what we did considered severing ties of kinship, and is it permissible for my aunt to avoid informing us about my cousin's news, and is it permissible for us not to communicate with my deceased uncle's wife?

If you blocked the number due to its peculiarity or fear of hacking, then you were not remiss. You should have explained the reason to your aunt to clarify the matter. If she did not listen, then sensible people should intervene to reconcile and remind her of kinship ties, concerning which Allah has warned us against Satan. You should strive to communicate with your cousin's mother to inquire about his well-being and maintain kinship ties with him through the customary means people employ, such as assistance, gifts, or visits.