Hiya,
Exciting day
I was going to ask - which company did you end up working with for importing the car and how much did it cost?
Noisy P/S pump - Replace fluid first, see if it makes a difference perhaps. Otherwise, a replacement can be sourced (try UK places like TopSpeed Automotive, John Wolfe Racing, US Automotive) and also Rockauto (U.S based and often works out cheaper, even with shipping etc.
Brake lights not working - The switch is by the pedal, near where it pivots. Make sure the switch is there and test it just by pushing it, sometimes they just need adjusting. Next, check the bulbs, obvious as it sounds. Still nothing? Check the fuses. The brake light and indicator are on the same circuit so if one doesn't work, neither will the other. If still nothing, wedge something, or put some tape on the brake switch to hold it to the on position, then take a voltage tester to the bulb socket and see if it's getting +12v. Also check the ground connection for continuity as this can be a common issue.
Indicators not working - When solving the above, it should solve this. you will need to rewire anyway as the indicators will flash red, which is an MOT fail. If there's not a write up on here already, either a 1st gen owner can help you, or we can take a look at a wiring diagram and work it out. It's not difficult to do yourself.
Battery not holding charge - Probably the easiest fix - get a new one
Check out Tayna.co.uk. They have loads of batteries, next day deliver and best prices i could find. Have bought 2 from them and very pleased. Don't go down the american battery route unless you've got cash to burn, or you're triyng to keep it concourse original. I made the mistake getting a battery from John Woolfe for £150! It was AC Delco but i could have just bought the same size with a much higher rating and performance from Varta, Bosch etc. for 1/3rd of the price.
Common areas for taking in water? (I know the boot is an issue and the heater core has been disconnected) Usually the bottom of the fenders, where they bolt to the chasis. When you open the door, there's a vent in the b pillar, remove this and run your hand to the bottom or see if you can see the area with a good torch. This is a very common area for moisture to gather. Inner wheel arches of the rear quarters - with the trunk open, you may need to slightly get in the trunk, then run your hand along the inner wheel arch, where it meets the quarter panel, as this is another common area. Also, run your hand to the back of the car, where the trunk panel drops down to the meet the bottom of the quarter. This a very common area for rust.
Any other questions etc. just let us know! Look forward to seeing some pics
_________________
How to post pics: When writing a message, scroll down and use the "attach file" option. Where possible, a photo sharing service can be used such as Flickr, Imgur etc. The image location (usually ending in .jpg) can be copy and pasted between the ][ brackets that appear when you click the 'Img' button (you can find this button at the top of the message box).
How to post youtube vids: Click on the 'youtubeHD' button at the top of the message box and in the middle of the ][ brackets that just appeared, copy and paste everything from the youtube web address that appears after the = sign i.e if this is the url:
https://www.youtube.com/watch?v=K2cNqaPSHv0 just copy "K2cNqaPSHv0").