Lol. Oh yeah, the groove was for a bar magnet I was going to put in. But I couldn't find as strong of a bar magnet as the little circle ones for the same price. That was just poor planning. I guess I could count it as practice for mortising since it was done mostly by hand (the round ends were drilled, the channel was chiseled out).
You could cut all the cuts with a coping saw or make straight cuts with a regular saw.
You don't need a plane, but I'd highly recommend investing in a hand plane. Look around for tips and suggestions for planes on this subreddit - it comes up daily!
You can probably find a decent plane at an flea market (where I got two of mine) or as hand-me-downs or even on craigslist. I got three from my dad - two are really nice - and the two from the flea market became nice after I read how to adjust and sharpen them.
For this kind of thing, if you don't have access to or can't afford power tools, I like a hand scroll or coping saw such as this one ($10 free shipping): https://www.amazon.com/dp/B00002X222/ because you have a great deal of control, the cuts are thin (less wasted material) and the tool is light weight.
You can also use a standard hack saw ($8 Prime): https://www.amazon.com/dp/B00B5A0T5K/
For manual sawing, I also recommend using a basic miter box. This one includes a clamp too, and can be screwed into something to keep it from moving on ya ($10.75 Prime): https://www.amazon.com/dp/B00009OYGB/
If you don't have a sander or a dremel for the edge smoothing, you can just use sandpaper by hand, but with all things manual, to make and finish 62 pieces of anything will just take longer.
Do let me know if you make a set for yourself! I'd love to check it out. :)
Edit: fixed a link and added miter box