Given a travel related situation, and given a specific question about the situation, summarize the question into a title

My old passport was damaged by a cup of coffee, so I have to renew it. It will take around 2 weeks for the new passport to come. But I'm in a hurry to apply for a Tier 4 UK visa.

The old passport was snipped by the authority and would no longer be valid. But all my personal information including the number can be recognized. And the number will be noted on my new passport.

Can I make an application or even an appointment with my old passport number, and get to the visa center with my new passport? 

It would be very nice of you if you can answer my question.

Can I make a UK visa application with my OLD passport number and wait for my new passport?

I think it's better if I tell a short example:

I plan on going from country A to country B, and I find out that it is cheaper if I pass by country X.
However, the flights from A to X and then from X to B have to be booked separately with unrelated airlines 1 and 2.

Is it usually possible to ask airline 1 to automatically transfer my luggage on arrival to city X, to the plane managed by airline 2?

Or do I have to grab my luggage myself and go through customs and airport-security?

Luggage transfer between unrelated airlines

It seems I will have a few hours to spend at the landside of Budapest airport. There seems to be a cafe Edit: http://www.bud.hu/english/passengers/shopping_and_gastronomy/restaurants/flocafe-8131.html but I can't find information whether it has power outlets. Although I have Priority Pass, all the lounges are airside and the only landside lounge I was able to find is part of a VIP package and as such it has a rather high price http://cavok.co.hu/pdf/pricelist.pdf and is not included in Priority Pass.


Power at landside at Budapest airport?