Thank you for taking the time and for being willing to check that, you are a great help here.
I have you covered and diagnosed here then.
1- the lock issue, not a big deal, the power lock actuator in the driver door is worn out. Very very common on the RX. The atuator is part of the latch assembly and contains the lock position sensors as well. All the problems you have with locking.unlocking and alarm are directly related to this. If the power lock does not move the lock to position then the alarm will not operate or set. For now what you can do is manually lock the car with the key in the door and then press the "lock" button on the remote to activate the alarm when you leave the vehicle parked somewhere. When you insert the key to unlock the door when returning this will deacivate the alarm as well. As far as repair the door panel needs to be removed to gain access to the assembly, there is 1 electrcal connector and 2 lock arms that connect to the unit inside the door, it is held to the door using the 2 torx bolts exposed on the latch side and the window track also needs to be removed to allow access for removal/installation, not an easy or fun job for a at home repair, keep in mind also that the master window switch is about a $800 part and easily damaged when removing to gain access to the door panel retainer screws. I would highly consider letting a Lexus or a Toyota dealer address this, the labor charge should be 1.5 labor hours, anything more then that and they are rippping you off. If memory serves me here I believe that the part is roughly $300????????
As far as your question on the driver mirror. This can be one of a couple things. Be sure that where the mirror housing swivels on the mount that is has no freeplay. Most commonly what happens here is that the electronic actuator inside the mirror develops freeplay and allows this to happen, Lexus considers this a crash part and only sells the entire mirror assembly so it is by no means a "cheap" repair, if this was my vehicle I would try to locate a used one in good shape (or just ignore it as I have my wife do on my 1999 RX )
As far as the window concern. I recommend spraying some lubricant such as "drylube" or spray silicone lubricant down the window run seal that the glass rides, it is common for these to dry out and cause the window to bind. Do keep in mind that with a binding window it also puts aditional strain and wear on the window motor, if this has been happening for a while the window motor may also need to be replaced.
Sorry for the delay it takes time to type out a detailed response. Please let me know if you need any clarification or additional details here. If this is all you need from me please hit the accept button before you log out so I recieve credit for my time, or simply reply back if you would like to continue ou conversation. Thank you again.