Advice on GAP Year

Hi monkeys,

I am currently 20yo doing my BSc. I was expected to finish by May 2021 but due to an illness that has befallen me and due to the postponement of my semester abroad I am expected to finish by Jun 2022. Unfortunately, by that time it is to late to apply for my Masters.

So I am currently planning ahead on how to schedule my GAP Year.

Jun/Aug: At first I want to do a summer internship, preferably at a BB.

Aug/Okt: Then I want to study for my GMAT as it can make up for my bad GPA (Expected 3.3-3.5; Top 10-3%).

Nov/Dec: Even though I want to work in M&A I would be interested in seeing how it is to work in management consulting. 

Jan/May: Doing two other internships preferably in PE

Jun/Sep: Travelling SEA or SA.

Now to my questions:

1) How would an internship in another sector influence my career expectations.

2) Can I afford to travel? I already have a gap in my CV (In July my semester abroad got cancelled and I had, therefore, a long summer break - even though I managed to secure an internship at an EB for Sep-Okt this was unfortunately cancelled too). So even though I have a legitimate reason why I have a gap I am honestly afraid that I wouldn't get invited to an interview if I have another gap in my CV.

3) Lastly and maybe most important, can I still break into IB/PE by the time I am 24/25? At literally all the internships I did, all of the analysts and most of the associates only had a bachelors and not a masters degree. They finished university by the time they were 21/22 and most of them will be associates by the time they're 24/25. Why would a bank still hire me then if I am 3/4 years older than the rest of the analysts?

thank you!