A student visa can also be complicated depending on the courses you're going to attend and the institution and amount of time you need it for. When you apply for a student visa 9 out of 10 times you'll be issued a 90 day visa (single entry, meaning once you're in Russia you can't leave and re-enter) and then after 90 days if your course is going to be longer the institution can extend it for a fee(not that expensive, maybe about 40 pounds, possibly less). After it is extended it'll become multi-entry allowing you to leave and re-enter as much as you want.

As for registration: You're obliged to register your visa within 7 days in Russia and if you travel to other cities/towns/regions for more than 7 days you're also required to re-register. I wouldn't worry too much about this because if you travel on a student visa the institution will register it for you, if you go on a tourist visa - your hotel will register it(or you can register it yourself at the offices of the agency who provided the invitation) and the latter also applies for business visas. You MUST inform them of the dates you plan to leave the country and inform them if these dates change because the visa must be 'de-registered' however this is usually done automatically based on the dates you say you will leave on hence why it's important to inform them if your leaving date changes.

It all sounds very complicated and painstaking but in effect it's not actually that bad. It takes about one day when you're in Russia and after that you don't need to think about it any more