Here are the mistakes corrected:

1. **People which care about animals will love this house.**
**Corrected:** People **who** care about animals will love this house.

2. **I want to live in a house whose garden are big.**
**Corrected:** I want to live in a house whose garden **is** big.

3. **There is a safety system who monitors outside the house.**
**Corrected:** There is a safety system **that** monitors outside the house.

4. **The ModHouse has lots of plants which keeps your home cool.**
**Corrected:** The ModHouse has lots of plants **that** keep your home cool.

5. **People whom have pets will like this house.**
**Corrected:** People **who** have pets will like this house.