Questions & Answers about Твоя забота о бабушке очень важна.
Because забота is a feminine singular noun.
Russian possessive words like my / your / our change to match the noun they describe:
- твой = masculine
- твоя = feminine
- твоё = neuter
- твои = plural
Since забота is feminine, you say твоя забота.
Забота is in the nominative case because it is the subject of the sentence.
The sentence means literally:
- Твоя забота о бабушке = Your care for your grandmother
- очень важна = is very important
So the thing being described as important is забота, and that is why it stays in the nominative.