Singer is one of the most popular brands so will be easiest to find parts for. Husqvarna and Brother are slightly less popular but still pretty popular. I’ve never heard of any other the other brands you listed. Some parts, like needles, are standardized. Others aren’t.
You can’t sew with two needles at once, but there is such thing as a double needle that’s used for special cases. More than likely you won’t need one. The second spool holder is most likely for 1) use with a double needle, 2) quickly swapping out thread colors or 3) actually a bobbin/spool winder and not actually for holding a spool you’re using.
As for stitch pattern symbols, each symbol is supposed to look like the stitch it creates. I would recommend trying to find a video showing all the stitches for whatever machine you pick. If you can’t find such a video, you can experiment with some scrap fabric.
So…the first thing you need to understand is that there are different types of sewing machines, as someone commented on your original post. There are:
“Regular” sewing machines, which can be either mechanical or computerized. These are the type of machines virtually all hobbyists use and can handle a huge range of projects, from linen napkins to ballgowns. It’s important to note that either the computer or the mechanical system determines stitch length and width.
Serging machines, which cut the fabric while sewing it, and make a single specialized stitch.
Embroidery machines. These are similar to “regular” sewing machines, but with a wider table and extra parts for stretching out the area you’re embroidering. They also have a computer to track/calculate the stitches in a given embroidered image.
As far as I’m aware, software is only available for embroidery machines. The computers in anything less than the most expensive of home sewing machines are pretty simple, and I’m not even sure how you would access them. They don’t connect to wifi, and there are no ports in the machines except for power and the foot pedal.
For the use cases you listed, I recommend a basic “regular” sewing machine such as this one. Any regular sewing machine built in the past several decades will be able to use a variety of stitches out of the box.
For repairing socks specifically, I agree with the other poster who talked about zigzag and stretch stitches.
My autistic dad frequently said that I was on the spectrum (always that exact phrase) but refused to have me diagnosed. I grew up just assuming that I had a high-functioning (as I need relatively few accommodations; my apologies if this is an outdated term) form of autism.
Now as an adult, I still don’t have the resources to get a professional diagnosis. I feel very much at home in groups like this; I have many of the symptoms of autism though not all; I got 136 on the RAADS-R test. That test was the tipping point that pushed me mentally from “strongly suspecting I’m autistic” to “self-diagnosed autistic”.