Yes, all trains in Britain are covered by a pass. London underground as well as metros and trams are not.

Do note that a single country pass does not include any trains to that country from another so for Britain the Eurostar from France/Belgium/Netherlands is not covered.

There are no reservations possible on the TfW trains that run to Aberystwyth.

If this is your only train journey then it would likely be cheaper to buy regular tickets, the cheapest London to Aberystwyth return is £73 for a walk up ticket (with some restrictions) and booking in advance can be as cheap as around £40 for fixed itinerary tickets.

Thank you so much for your answer! 

It's not my only train journey, because I'm staying over at a friend in Aberystwyth. 
We're planning on travelling through Wales as well. 

So those trains are also covered, as I understand?

Depending on prices and what trips in Wales you'll make, a return to Aberystwyth and a rover ticket for the region may also be an option:

https://www.seat61.com/train-travel-in-britain.htm#rail-rovers

And what about the buying of the pass? You can buy it a month beforehand or do you need to buy one way before the summer then?

You can buy a pass whenever you like. No need to rush right now, you can e.g. see if here are any Interrail offers in February or March (this is often the case).

Yes, all normal trains in Wales are covered but as above it may not be the best or cheapest way to travel around that region, there are also a number of heritage/steam railways dotted around Wales that are not part of the pass, there is even one in Aberystwyth if that sort of thing interests you.

For travelling around Wales by public transport, particularly the west/central regions there are very few railways, in that area there is only the Aberystwyth line and the scenic Cambrian that branches from the Aberystwyth line at Machynlleth.

if you are going to be based in Aber then you will probably be better mostly using buses and there are some good cheap tickets available for that. For example all buses in the north of Wales as far south as Aber are covered by a day ticket costing £6.50.