New Owner needing advice

Just bought my first discovery to replace my Focus ST (bit of a change!) due to me now living on a farm i needed something a bit more practical.
I picked up a 2002 (52) discovery XS at the weekend and overall im fairly chuffed with how well it drives and how after a 2 hour journey i didnt want to cry. Its done 153,000 so i didnt expect it to be perfect but theres a few niggles i want to get sorted.

1 - when you unlock the car all doors unlock except drivers door, you cant pull the lock tag thing up it wont let you, but you can open door with the door handle on the inside. What do i need to replace?

2 - In second gear it is extremely juddery at 3-5000rpm and i mean extremely fine in any other gear.

3 - When braking (if i brake very slowly to a stop its fine) with force, not emergancy or anything just reasonable like slowing down for a junction the steering wheel shakes quiet badly. Tracking is fine do i have warped disks?

4 - steering wheel is a little bit juddery when cornering sometimes, i noticed on the MOT there were a few advisories including something wrong with a power steering component. doesnt give details. and also 2 brake pipes were corroded not sure if that will by anything to do with problem number 3.

Any help on any of these issues will be massively appreciated, they may be common faults but right now im new to the disco world!

Kimmy

1
) Not sure, but probably the spring has bust. Fiddly but possible
2)Not sure
3)+4) Check all you steering components eg.track rod ends, and your brakes and discs.
5) Welcome to the wonderful world of Landrovers

2/ could be a uj
3/ if you had warped disc,s your pedal should go up and down abit when braking
4/ i bet the box is leaking hence why it was picked up on mot

oh 1/ sounds like the spring is on the way out (as said above

If it is a UJ will something like this be right

LAND ROVER DISCOVERY 2 1998 TO 2004 DOUBLE CARDAN FRONT PROPSHAFT REPAIR KIT | eBay

or ive looked on ebay and you can find single ones for about £8

That would service the front propshaft...but you do have a rear one as well

Check warped disc(s)

Only juddery in second? Fine in the rest. Could second gear(s) have had some teeth chipped ? When the syncromesh wears it's usually 1st to 2nd changes.

Diff.

the gear changes are absolutly fine its when your accelerating only in 2nd.
i have to do both think ill let the garage work out what needs replacing before i go buy all these bits and bobs haha!