Two problems with brand new Mac

Just got a new, pricey MacBook Pro, about a month ago. Anyways, I'm having two strange problems.

Firstly, my MacBook Pro keeps turning off randomly (which is pretty annoying when I'm trying to take notes on it in the middle of a university lecture)... weirder yet is when I start to close it and it's just slightly open it will turn back on but when I open it up fully again it turns off. This issue presented itself to me about 5 days ago and was messed up like that for a whole hour lecture. Then, it seemed to work fine but today while I was on it the issue persisted suddenly again. Now it's working fine, so I'm a little confused as to why it does this.

Secondly, yesterday I downloaded some slides from the profs site but it won't let me open them. I tried downloading other notes, from other profs and now none of them seem to open - just last week they would all open. Along with this my Mac is having trouble opening one of my screenshots of my course calendar.

I'm not a computer guy so maybe I'm just doing something wrong in either cases, I don't know.

Thank you in advance for any advice