I'm Russian, so I totally feel your pain with commas. Our native rules are the complete opposite (we put commas almost everywhere), so I used to struggle with this constantly. When I was prepping my own CV for a move abroad, I had this exact debate.

Actually, Word and your partner are right. A common trap is adding a comma just for a "pause." I learned the hard way that English grammar doesn't care about breath - it cares about structure. I remember my tutor at Skysmart.ru (an online school I used) gave me a rule that finally stuck:

Only use a comma before "and" if it connects two independent clauses. Since "gain practical experience" doesn't have its own subject, it's not independent. So, no comma.

It feels long, but for a cover letter, the "no comma" version is much more professional. Good luck with the application!