Here are the corrections for the sentences:
My family and I lives in Bern, Switzerland.
Correction: My family and I live in Bern, Switzerland.My sister has got a guitar and a violin.
Correction: No change needed.My brother really love football and basketball.
Correction: My brother really loves football and basketball.I like the colour purple, but I don't like orange.
Correction: No change needed.My cousin is 14 years old and I is, too!
Correction: My cousin is 14 years old and I am, too!My grandparents has got a house in Italy.
Correction: My grandparents have got a house in Italy.