Gujarati phrases for meeting his parents
If his family speaks Gujarati at home, Hindi will be understood and Gujarati will be felt. You do not need much. A greeting, a line about the food, and an honest admission that you are learning will get you further than a memorised paragraph you cannot follow up.
Walking in
જય શ્રી કૃષ્ણ is worth knowing even if you do not use it yourself, because it is likely the first thing said to you. Answering with the same words is completely normal.
Introducing yourself
Notice મારું, not મારો. Gujarati has three genders where Hindi has two, and નામ is neuter, so the possessive takes the neuter -ું ending. This is the single most common place a Hindi learner slips in Gujarati.
At the table
You will be fed more than you asked for. બસ, થોડું જ is the polite decline, and it is more useful than any compliment, because you will need it three times.
When you lose the thread
Leaving
One difference to hold onto
Gujarati looks close to Hindi and then swaps two endings on you. -ને is the object marker, doing the job of Hindi को, and -એ is the ergative, doing the job of Hindi ने. If you read તમને as an ergative because it looks like ने, every sentence comes out backwards. તમને મળીને means "having met you", not "you met".