I run no more than two cables, 12-2 or 14-2, through a 3/4" hole. Your 12-3 should be by itself passing through the stud, as another cable could cause binding and abrasion damage to the cable sheath. Multiple 3/4" holes through the center of the stud will not appreciably weaken it, as long as they're not close to a large knot or other cut, notch, split, etc. The common neutral configuration will not give you problems as long as the GFCI is downstream of where the neutral splits to two circuits. Bringing the wire through the drywall and cabinet frame into the fixture would be my choice, as long as the fixture is designed for romex connections.

Undercabinet LED lighting is a great DIY project... Here's what I did. Works out to about $5/ft. Links below are clickable. Here's a video below - this guy used connectors - I thought soldering was easier and cheaper. Installing undercabinet LED strips I suggest watching other videos also, search youtube on "led under cabinet lighting installation" and you will find several. I installed about 2-1/2" from the face of the cabinet to avoid shadows. You'll need 120V for the power supply. Lots of different type LEDs - brightness, temperature (color). Here's a list of the things I ordered from Amazon: power supply - $9 LED strip lights - $15 for 16 feet 26 gauge wire - $7.60 for a spool to connect the LED strips (solder) Aluminum channel diffusers - $27 for 5 pieces of 1 yard each Dimmers - $10 for 3. Optional parts. I never seem to use mine. Since then I've added LEDs to my RV, a closet or two, and plans for more.

Sophie, It's not that I am not up to it. I have never heard of it and when I did a search of Hafele, this is what I found: https://www.hafele.com/us/en/product/flexible-strip-light-loox-led-2015-12-v/0000000b0001949900020023/ I just don't understand how it is used, and I don't need such large quantities. You said no installation by teenage son. He has installed a front door, a ceiling fan, several light fixtures. I guess if you don't think he is capable, I wouldn't be either. So maybe I am not up to it. I don't know enough about the product to be sure. I guess I'll go to youtube.

I didn’t do led tape but in my laundry I installed this low profile under cabinet light and really like it. They can be linked together. They are hardwired but you can also order a plug for $10. There’s an on-off switch but I put mine in a wall switch. Also you can direct the light on the unit. And there’s a set here to change from 2700 to 3000 depending on your need and preference. The piece that I’m touching tilts so you can direct the light. The problem I’ve seen with tape light without a shroud is seeing the reflection from the individual diodes. I am going to install WAC tape for above my bathroom cabinets but they are so expensive. I’m still looking for a lower priced option for my shoe cabinet in closet. Too large of a run for the WAC $ Good luck!