1. A drawing tablet is not necessary for vector drawings. It only comes into play when you are following a workflow similar to the one here where you sketch something and import it into Inkscape. Even in such a workflow, you can make do with a scanner where you can sketch on paper, scan it and then import into Inkscape.

2. I cannot say for others, but I do use it extensively. I have almost stopped using the touch pad/mouse - instead I exclusively use tablet. The reason for this is, part of the time, I spend doing digital paintings. I have gotten quite comfortable with it that I use it whiled doing vector illustrations too.

3. I don’t think you can do everything in Photoshop that can be done in Illustrator. Photoshop can do some things that Illustrator can do, but at the end of the day, Photoshop is a raster editor and Illustrator is a vector editor. Even though you can use some of the vector tools in Photoshop, it would not result in a vector illustration (like AI, EPS, SVG) - instead would be rasterised.

Hope this helps. Thanks for dropping by.

Also

Do most vector artists, from beginner to amazing, use drawing tablets?

and lastly

Can I do everything in Photoshop that can be done in Illustrator?

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