Will HR check my exact diploma title and internships in my resume?

I started bachelor of computer science, but it was too challenging,my GPA went down, it was very low and I was failing to meet min.GPA requirements. So I switched to Math, graduated with “3 y general degree in Math”. Though I started as Computer science student and completed some CS courses, my last year was pure math courses.
I have been working as front-end web dev for 1.5y.
I want to work in a tech giant company(FB, google etc)

Also, I did not do any internships during my bachelor’s. Can I add in my resume that I had some 1-2 internships in startups?
Will they run some check?
1)check exactly diploma title
2)check my internships?

Probably not

For big companies (FB and Google), my guess is probably.

FYI - What you are suggesting is highly unethical and if the company ever found out/figured out you lied, you would be fired immediately and you would lose out on any good references even if your work was good. Honesty is always the best policy. Plus, if your development work/portfolio (assuming you want a development job) is solid, the diploma and your exact GPA is less important. They could ask for copies of your transcripts (thought not always), but most of the time they just want to check if you actually graduated with an actual degree. The degree shows you have the capability of finishing something you start.