Few problems with my 106 please help!!

ive had my 106 for just over a year and I love it to absolute bits, only thing is it’s had a few electric problems I can’t figure out how to solve and would appreciate some help

1) my rear window heater doesn’t work? I press the button in and it will light up slightly but will come out as soon as I let go.

2) every so often when I indicate, whichever way I’m indicating will flash normally but the other side will sometimes flash quite sporadically?

3) is there any way to make my cigarette lighter only live when cat is on with ignition as I have a dashcam and it’s quite tedious plugging it in and unplugging it every time I use it.

Any help would be massively appreciated!!
I’ve checked all my fuses and they’re correct and working ☺️