Well the easiest thing for you is to come on your British passport. No visa required (for 30 days)

If it's your first trip to Thailand it's overwhelmingly likely that the biggest problem you will have is with the airline you're flying with, not with immigration.

Assuming your flight is at 16:00 and it is on time, then that is more than enough time to get up to the border. There is not, AFAIK, a minumum stay requirement in Laos, but you will need to buy a visa for Laos, which will cost between $30 and $50 depending on your nationality (there are a small group of countries that get visa free entry to Laos, however). Make sure you have US$ for the Laos visa, as, though they accept baht, they give you a very poor rate.

Re Q2, at present there is no need to report to immigration every time you arrive in the country if you live in BKK.

You can theoretically be asked for "3 proofs" (cash, onward travel, accommodation) any time. In practice it seems that people who have a history of back to back stays on TVs or visa exempts are the ones who tend to get asked

@Jeremy *****

Yeah, I meant to comply with the 'Must show 20k baht or equivalent rule'. I know that you can easily get rid of your INR in Bangkok. It was more 'if you want to be sure that immigration will accept the currency you show them, get some US$ or Euro when in Indonesa'

If you want to be 100% sure, then change your INR to US$ or Euro in Indonesia. This will be better value than getting baht there or getting rid of INR here...

Sorry, but that's not true. I changed a fairly large amount of INR at Don Mueang a couple of months ago

AFAIK the wording is 'major convertible currency'. Considering that the SCB counters immediately behind immigration DO change Indonesian Rupiah, one would assume that it counts. However, this is Thailand...

Right, you DO NOT need to go to a police station if you're going to leave the country (as opposed to going to immigration for reporting or extending, which is a different story). Just rock up at the airport, get a new one and fly out. Simple as that.