Certainly!
If your course has a mandatory year abroad (which I imagine the language courses all do!), then you will be guaranteed a study abroad place and will be able to apply for universities from a set list which meet your course requirements. For example, the options for my course were Nancy or Lyon and I applied for Lyon as my first choice of university. My course was very niche though - generally language students have more choices than just two!
For courses which do not have a mandatory year abroad, you apply for universities from the master list of unis. However, if you were, say a Law student, you would only be able to apply for the ones which accept Law students/students from any course. The year abroad is not guaranteed but I think the vast majority of people are offered a place, even if it was not for one of the unis they applied for.
The study abroad office is really well-organised (or at least it was when I was there!). They run talks throughout the year, both before the application process begins (e.g. on how the process works, tips for how to choose and apply for unis, etc.) and for those that get a place (e.g. on finance and funding, travel tips, country briefings from students who previously studied abroad in that country, etc.). I studied abroad in 2019/2020 and they were incredibly responsive and supportive when Covid hit and we needed to come home suddenly.
Re societies, Leeds has so, so many! You can browse them all here:
https://engage.luu.org.uk/groups. At the start of uni, clubs and societies will be hosting Give it a Go sessions which allow new and returning students to try out the club/society for free (or sometimes at a very low cost).
I hope this helps!