The dash cracking is mostly uv damage from the sun and expansion/contraction between hot and cold. Usually in the winter the car sits at -20 and then you crank the heat to 100 and it expands rapidly.
In northern Quebec I actually had some minor dash explosions lol Sitting at -40 then warming up too quickly caused the cracks to pop little bits of foam all over the place.
I would use something that moisturizes vinyl and protects against UV damage and apply monthly. For the first application slap it on thick and let it sit for a few hours. Then wipe excess off. Give it time to absorb. Pick a decent brand like autoglym.
Actually I just read MaxBell's comments and he's right on the money...
Well the locks are electronic. Does that door unlock when you use the other door or trunk to open the locks?
Shifter - Take the shifter boot off. Check that the shifter is centered in the hole properly. MaxBell is right again in that the bushings are most likely worn out. To be exact, if the whole thing moves too much it's likely the rear bushing (towards the back of the car) that has let go. It's a cheap part but a pain in the ass to replace.
If you have an 325i the shifter should look like this: (part #2,4 and 7 should be replace in the least).
On older cars there is a plate and a horrible rubber mount/damper. And it looks like this:
A lot of guys might bite my head off for showing you two but the reality is these cars are old, and since the parts are interchangeable in many cases you won't know what you have till you look. You most likely have the first one above as that is the standard for an 'i'.
I'm only mentioning this because some 'i' cars start out as autos and are converted to manual. They could have easily used 'e' transmission and shift components.