I did all the lights some time ago (have a look into my garage) but didn't take pics along the way .... anyhow, the dome/map light assembly comes down pretty easily when pulling on the rear corners down - use a pry tool first so you get a little gap that allows you to grab in with the fingers .... disconnect the plugs and take the whole assembly to your work desk - vieing it upside down the lamps are housed under the black plastic cover (as you already know) - to take that of securely take a flathead srewdriver and gently disengage where you see the little noses. Also have a look at the appendix of the user manual - that for some reason is only available online (I do have the german version only, so doesn't make sense to post that here).
Regarding the "rest light" you see, there is a problem with your leds that obviously have not the correct resistor built in (I bought mine here www.hypercolor.de
). They should then be off completely after 20-30min, when the "remainig current" has dropped to Zero. So check that. Otherwise I'd go for other leds.
As for the vanity mirror lights - as this has been asked in this thread as well - here also the whole assembly has to be taken out - pry from the right hand side - hold the gap with your finger and then pry gently around the bottom corner all the way to the left side and the mirror will come out - flip it and take off the inner plastic (again with a srewdriver) - see the pic for what it looks like. Now you can take out the bulb ...... hope this helps a Little.