The objectives embossed with numbers that begin with an A, B or C etc. are 160mm tube objectives. The one beginning with a C is a coated objective. Those are serial #'s not model #'s. Those all date from the 1950's or early 60's.
Dark M is a 160mm tube phase obective. Dark M means ; dark phase, medium contrast. There were 26 such objectives( maybe more) for the 160mm series 2 and 4 scopes, all marked with specific details as to type of phase: dark,bright or B-Minus plus in the early days, the lambda shift, then later converting that to light, medium or high contrast; L,M or H.
The objective you have noted as 36X is in fact a 3.5X 0.9 objective for the 160mm tube system. The number is probably poorly embossed or damaged.
You could probably build up a decent series 4 phase scope eventually, with scope # 5. There is a condenser on ebay. It's been there a while and the seller would be lacking in common sense, if they didn't grab an offer on that. Dark M objectives are the most easily found, so a set shouldn't be too hard to put together.
You will require a 6v. power supply like this for that scope, unless you want to change the plug and use another type. The original power supplies are sturdy and seldom fail unless used to death.https://www.ebay.com/itm/AO-American-Op ... 518cbc14e6
Microscopes 1.2.and 3 all have the series 10, earlier ,18 watt tungsten illuminator. These also require a remote power supply but the plug is different than the above. Either will work with either, though as long as the plug is converted to the correct one. Power supply:https://www.ebay.com/itm/AMERIACAN-OPTICAL-AO-1051-MICROSCOPE-POWER-SUPPLY-211659/233277104098?hash=item3650661fe2:g:uOIAAOSw-NBdG7AF
Microscope 6 has the later 20 watt halogen illuminator with a built in power supply. That one should light up when plugged in and turned on. The pots sometimes go( it's a standard one used in many things...there is a thread about it here from a year ago or so).
The bulb sockets sometimes lose a bit of contact at some point, arc a little, oxidize a little, and over time the situation gets worse, with a little extra heat. That microscope is 40 years old or so, so no telling what the situation is. Some dealers still have new sockets ...Martin Microscope is one.
What I would do is first test the focus on all of the series 10's. Pick the one with the smoothest focus. Then check the stages and pick the best.
#1 has a left hand stage and a left hand slide carrier. You may want that. They are fairly rare. If you don't want it, tighten everything up, clean it up and sell it on ebay as a unit. Somebody out there wants it.
Check the condenser carriers and choose the best.
Phase condenser may need reconditioning. There is a good chance some of the annulus adjusters are rounded out. They can be replaced but getting them out is a bit of work. Top surface of the phase condenser lens might be euchred . Sometimes , users were sloppy, removing and replacing them, dragging the lens against the bottom of the stage.
# 1 and 6 have 5 place nosepieces. Those are great, because you can put in a 4,10,20,40 and 100.
Your best BF objective complement is 1) 4X # 1017. 2) 10X # 1021 3) 20X 1022 4) 40X # 1309 5) 100X 1079. That's about as good as they had in planachros except for the 1079 until they went over to 45mm D.I.N. I would be looking for an inexpensive # 1029 or 1311, 100X planachro. The 1079 was an excellent objective and was made for almost 40 years. It is close to plan but the later planachros are better. If some of the same objectives are about the same condition, check them all out and choose the ones with the closest parfocality. There will be small differences. You will have to use the # 1309 objective as a base line because you have only one.
Looks like you have only one trino head but you have the tube with it. Best eyepiece for the tube is either a # 1054 or # 437. Both are focusing types and take reticles. Remove the reticle, if there is one. You will need an adapter that can clamp to the upper portion of the tube and then be adjusted along it's length for height. Macro rings and or distance pieces can be used to get the correct eyepiece to sensor distance. It is around 55mm, depending on your sensor dimensions. You can get full coverage of the frame and parfocality with such a system. I use a small mirrorless camera up there with a 3.00 electronic shutter release.
No vibration and well corrected images. You can get away with using a spare # 176 eyepiece in the photo tube but the focusing feature plus field characteristics of the aformentioned ones, I like better.
I have tried several incarnations of Leiz Periplans in a series 4 without much success. I tried the versions corrected for the 37mm 170mm system, the 45mm 170mm system and the 45mm 160mm system. All of them gave poor peripheral corrections when the series 4 was fitted with it's compensating lens above the nosepiece, as it should be. Without it, I don't know. My guess would be that the Leitz Periplans in a series 2/4 with AO objectives would be malcorrected, without the compensating lens too.Most of them have a narrower f.o.v. too. The correct optics are cat.# 146. 10X and Cat.# 147 15X.
The series 10 microscopes use cat.# 176 or 176A 10X and cat.# 184 15X.