Yeah, if you study fine at home with no issues there's nothing wrong with doing that.
Best to do it where you're most comfortable and able to get into the zone. Some of my friends have never even set foot in it lol, but personally I like the library as the student house I'm in can be quite noisy and I'm likely to get distracted with my housemates or own devices, whereas the library's a "work setting" where I'm less likely to slack off (though still do sometimes
); also psychologically it's nice to be able to have a separate work space, coming home to relax and do other things. It can also be good practice for working in an office environment and gets easier over time; trust me, no one's gonna be looking at you in the library, they're too busy trying to sweat out an essay before a party or whatever haha.
Glad you're fine with courseworks, as I said it's best to start them early and chip away at them overtime but I'm assuming you're hopefully not a last minute person like I've only recently stopped being lol. As a bit of a lazy sod but who's good at memorizing stuff I tend to do better in exams myself but feel coursework's generally a better way to assess ability and put skills and knowledge into practice to be honest (simultaneously a 100% coursework course would probably be too stressful!).
As wonderland.16 mentions practice runthroughs can definitely be a good way to practice for exams and help to alleviate anxiety therewith. If you ask I'm pretty sure you'd be able to practice papers in the exam rooms when they're not in use. I had a friend in secondary school who did something similar for A levels, asking if he could do past papers in the exam hall after school, so by the time the real exams rolled around it didn't stress him out, he was used to the exam hall setting (obviously other students will be there for the real exam but doesn't make a difference when everyone's focused on their paper) and did really well! But yeah, preparation is key in reducing anxiety so long as you've revised, nothing to worry about
(and if you haven't, wing it
I'll admit I barely studied for my exams in first year lol).
Chillax for the stats exam; whenabouts is it? My advice, try to understand all the material and then do those past papers, and you should be totally fine.
The first exams might be a bit daunting but you'll get used to uni exams, and if you're having trouble with exam anxiety etc. let the uni know and they can hopefully offer some support with that. Anyways best of luck with the rest of first year and most importantly try to enjoy it!