Some not entirely accurate or slightly out of date answers on this thread.
Moscow and St Petersburg are in the same time zone. You can get an overnight train between the two, but there is also a high speed day train that takes just 3.5 hours.
While it's still not super vegetarian friendly, there are more places now that cater to it, e.g. www.inyourpocket.com/moscow/restaurants-and-cafes/Vegetarian Incidentally, lots of Russians go vegetarian - or even vegan - for the duration of lent and restaurants cater to this, but that won't help you if you go in October.
The In Your Pocket guides for both cities are generally pretty good, up to date and free.
The exchange rate with the pound is a lot better than it was a few years ago, and a lot of things are generally very cheap (including public transport, taxis, vodka, beer, local food). Anything imported and seen as fancy has a premium (e.g. Wine, foreign food restaurants aimed at the rich).
Google Russian visas and you will find lots of agencies which can talk you through the process and provide any necessary paperwork.
Russians do tend to be a bit cold to strangers but extremely warm to friends.
It's a great place to visit, and enough people speak enough English for you to be able to get by (plus more and more signs, public transport announcements etc are now also done in English). But if you are not usually adventurous travellers, you may enjoy it more on a group tour.