I have seen some TOCs advertise for part time gateline / station / ticket office staff - e.g. doing just morning or afternoon peak (don't know how well this would fit round studying)
I've not noticed any advertising for weekend only staff but some might.
I have never seen adverts for guard / conductors on a part time basis.
At the possible risk of stating the obvious, rail replacement bus / coach drivers are not employed by the train companies.
Generally speaking, a TOC will either have an in-house team which organises rail replacement services, or will outsource this - sometimes to another subsidiary of the group (e.g. most First TOCs go through First Rail Support, Southern / Thameslink GN and South Eastern rail replacement services are mostly arranged via a team within Go-Ahead's london bus operation.)
These organisations then sub-contract the work out to bus / coach operators - sometimes (as Go-Ahead London do) covering what they can in house and contracting the rest out. Each sub-contract can be as little as one coach on a one-off journey.
You can - in some circumstances - drive buses / coaches at age 18, but you're limited (from memory) to either 16 seaters or full size vehicles on 'domestic hours' work - which is services of less than 35 miles until you're 21 (or it may now be 25). In other words, bus not coach.
Not all bus operators will even consider taking on 18 year olds and putting them through the PCV training / test, those that do will generally want you to work full time for at least 2 years after passing (or they will want something towards training costs)
Having said that, I've today seen something to suggest Reading Buses are seeking university students as trainees for part time driving (presumably evening / weekend) jobs.
Rail replacement control / customer service work (it depends which company you're with what the balance of control / customer service is) tends to be peaked at weekends
people doing that are a mix of full time transport workers doing it as overtime, people who are semi-retired or have other jobs, and some students. This may be a way in to transport work (although bear in mind much of it will involve either early starts or late finishes) - and some experience of customer facing work / solving practical problems is likely to be an advantage.
The controllers tend to be employed by the likes of First Rail Support on a casual basis.
If you want to give a clue where you are, I may be able to point you in the direction of local rail replacement provider/s.