You can do this job with your circular saw. As suggested, clamp a straight edge (another piece of wood with a factory cut straight edge or a long level, or commercial edge guide) to make the cuts.
You don't need a stair tool for this retrofit. A tape measure will do fine.
You should have a level and speed square to check for plumb, level, and square.
My favorite sawhorses are the Bora Speedhorses--quick to deploy and compact when put away. Though any solid sawhorse will work.
Here is a decent video on retrofitting stair treads:
https://www.youtube.com/watch?v=9iOsbprpe5g
For the ballister cutouts use a jigsaw. Or if you have skills a Japanese hand saw.
Some newer construction stairs have the tread cutout so that the carpet lays in flush. This height difference would need to be filled in.
One tricky area may be the top landing. Will this remain carpeting?
Any construction adhesive will fine (Liquid Nails, Loctite, Gorilla...)
Another thing to consider is building code for your area. Codes are stringent about the rise and run of stairs. Make sure the retro risers don't put you over the max height.
Good luck with your project!