Antique headboard and footbard with iron frame

That is a ceiling light mounting plate, used with knob-and-tube wiring.

The flathead screws would fasten the plate to a ceiling joist, and the wires were fed through the larger holes. The center hole is intended to support the weight of the light, via another part that is missing from your example.

I think the setscrews held small insulators, probably ceramic or bakelite.

Two of the wire holes are opened, and the other two still have their knockout plugs in place. Four holes were needed only when continuing the wiring to another fixture.

Knob-and-tube wiring, and fixtures like these, are now obsolete and may not be legally installed in the U.S. Existing Knob-and-tube may be left in place, but not extended or modified. Any changes require complete replacement, which was probably done in your friend's house at some point.

Given your expressed degree of inexperience, unless you particularly want the learning experience (good, but pay close attention to coming out the far side with all the fingers and eyes you had going into it, and don't forget the earplugs for preserving your hearing, too) your best bet is to take a sample around to a custom millwork shop, which can likely do the job easily.

Aside from the "never used" aspect of your tools, the quaint belief that there's 3-3/4 inches of lumber in a 1x4 is concerning regarding how much of a learning process you have ahead of you for the DIY route. You MIGHT be able to get 3/4" thickness from 4/4 hardwood, but you often need 5/4 to be certain (fortunately you only need the one side to be good, which improves those odds - leaving the backside not completely planed is OK) and you'll definitely need 4-1/2 inch width to have 3-3/4 inches to work from. A "modern 1x4" in S4S condition (surfaced, i.e. planed flat, 4 sides) is typically 3/4, or even 11/16 thick (13/16 if you get a really super supplier) by 3-1/2 wide.

If you choose the learning experience, expect to make some bad boards, especially at first, and again when you get overconfident. That's part of the experience, and the only way to get experienced is to do it, learn from it, and do it some more while remembering what you learned when you screwed it up. But do try really, really, hard to make sure that your learning experiences don't involve trips to the Emergency Room.

Square- section T&G can be difficult to assemble. This is a set of routerbits that cuts a wedge-shaped profile (which has implications for "fixed size" that should be obvious) - I have also seen more rounded profiles, but am having no luck finding a set of router (or more commonly, shaper, but you don't have one) bits to cut those at the moment.

For the limited amount you need, you could just sand sharp edges off the tongues. You could also cut the square tongues to a rounded profile with a cove bit and a fence on the router table.