EEA family member visa VS summer internships

Good morning,

I have a few questions regarding the EEA Family Member Visa:

1. Firstly, is it equivalent to or different from the "Family Permit"?
On my Visa it's written "VISA EEA FP: FAMILY MEMBER To Join [parent's name]".

2.1. In either case, would my current Visa allow me to do something like an undergraduate summer internship program in the UK, or...
2.2. Would it be legal to apply while I am already in the UK, go for interviews, assessment centers, etc. or...

3. ...would I need a separate Visa/Work permit to do so?

I do not want to migrate, but my parents (EEA nationals) live in the UK and I (non-EEA national with permanent residence in another EEA country) often visit them when I'm free, therefore I often go to the UK with a EEA Family Member Visa (6 months validity).

Thanks a lot!

You have an EEA Family Permit and that confirms your right to live, work and study in the UK. You do not need "a separate Visa/Work permit".

If you are intending to live in the UK, rather than just visiting, you will need to apply in the UK for a Residence Card, so get confirmation of your continuing right to exercise Treaty Rights in the UK.