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Made the border crossing into Estonia at Ivangorod-Narva by Simple Express bus. Nobody even batted an eyelid for the registration.
Also in St.Petersburg, the hostel I stayed at said the same thing - You do not need to register if you are staying at one place for less than 7 business days.
So I guess that rule is widely known. For all the other people out there who are worrying about getting registered, just keep your travel receipts / tickets to show if you are questioned (in the rare case).
Upvote:1
This was resolved in chat. I will leave a basic summary here for anyone who was following the question.
Chat summary
The cost of registering depends upon the local authority; I would guess in Murmansk the cost would be about EUR 5; and in Peter it would be about EUR 20. But those are guesses whose purpose is to give an indicative range of what kind of money we're talking about.
The fine for not registering is about EUR 100 and may possibly attract a ban of 5 years. For those wanting to lie about having registered, leaving by air is a whole lot more risky than leaving by train.