Water cooled is standard for diffusion pumps, and shouldn't take too much to cool them, especially one of that size that is not too large. For comparison, my 850W EO6 diffusion pump with an inlet diameter of 5" requires 75 L/h or .27 gallons/min cooling water flow at 20C, which is very easy to find a pump with that flow rate for cheap and cool at those requirements. A simple heat exchanger can even be made with some lengths of 8020 with water flowing down the bore holes and externally cooled by fans. Obviously if you have built cooling supplies for liquid cooled computers the concept should be fairly similar, and it never hurts to do a quick thermal load calculation to validate your setup (or simulation, another reason why I strongly advocate learning Fusion360.) If you are worried about cooling, you can also easily monitor the water temperature with the appropriate sensor and read it out with something like an Arduino, and even interlock the diffusion pump power if the temperature climbs above a certain set point.
The inlet flange looks fairly standard. A lot of diffusion pumps inlet flanges are ISO or ASA compatible - my flange is an ISO160 compatible flange. I would measure the outer diameter of the flange when you get it as well (I assume you already purchased it since the link goes to an ebay listing that has already been bought.) For a 3" tube ID, that correlates to an ISO 80, but you should always measure yourself and double-check (including the center to center diameter between mounting holes.) It also looks like it could be an ASA flange however - for that size, you generally would have 4 mounting holes, as does the one you have. Again, you have to measure everything to determine the compatible standard.
That being said, an adapter plate would be very easy to make, and can be quite simple depending on your chamber. For my system, I am using a 1"x9"x12" plate of ATP-5 aluminum plate to go from my 5" inlet to my 2.75" conflat based chamber. Just mounting holes for the parts, no grooves needed in my design. The center hole is 1.5" through, and the 6 holes around it are blind-tapped to bolt the conflat part to. Everything else is through-hole for mounting the diff pump and to 8020 supports on the side:
The diffusion pump has an o-ring can seal to the bottom of the plate, and I will be using a flat cross-section viton o-ring on the top between the plate and the 2.75" chamber. My current design will have a water-cooled baffle, so I will need an additional adapter, but they all stack and work identically. You can see how I stack my design here:
From a NASA paper I found regarding design criteria for elastomer o-rings for high vacuum chambers used in space simulation, the surface roughness of the o-ring gland and mating surfaces should be 32 micro-inch or better. ATP-5 aluminum has a maximum surface roughness of 25 micro-inch, so the plate will work as is without need for further surface machining, and is not as expensive as some of the other higher-tolerance tool-plating.
I have designed similar plates for chambers and flanges ranging from 2.75"CF all the way to 10"CF, and various other very large sized ISO and ASA flanges between my pump and other components. I have not used them, just planning out CAD models and designs, but I will be having the above plate machined soon and ready for when I start assembling my system in the next coming months.
A few things upon receiving the pump if you bought it. First thing, as mentioned above, check the heater. You can get replacement heaters, but its better to just return the pump if it is in poor shape and not working well, especially if you have no info on the pump. If you decide to keep it, you will definitely want to clean the stack - it looks like there is black gunk all over it which is not good, especially if the jets are clogged. If there is that stuff all on the inside you will want to clean that as well. Also, the forepump port seems less than desirable - usually there is some sort of mating flange such as a KF flange, which may make things challenging if you want a leak-free seal, and it is not threaded or looks like there is much of any attachment besides a tube. You can however look into possibly using a compression fitting to KF adapter like here: http://www.idealvac.com/subcatagoryb.as ... on-fitting
. That may be a very simple and easy vacuum tight seal with a KF attachment point, though it depends on the tube OD and if it is compatible with any of the standard sizes.
Personally for me, I would hesitate to purchase the pump without knowing as much as possible about it. I also have a very restricted budget I am working with, which necessitates me to make sure that each part I buy has the highest probability of functioning as expected, especially since most of the stuff is purchased used off ebay for myself as well. That means many many hours of research and planning ahead of time. The fact that there is no part number or manufacturer would make me hesitate - I would want to at-least find a datasheet if possible, since I heavily calculate the vacuum parameters of my system and I would need to know at-least the pumping speed of the pump prior, in addition to the power consumption and cooling rate required. Also, the pump seems a bit gunked up and dirty on the inside - easily cleanable but possibly a sign of misuse. For my vacuum system that I am currently designing, I have taken maybe a rather extreme engineering approach, which includes months of budget planning and optimization, based on all available parts and costs, followed by several design iterations, and finally some backing calculations to make sure everything is in order or I at least know as much details as possible about my system before I make any purchases. It really depends on what you want out of your system though - for simple brute forcing neutrons with a fusor, surprisingly little is needed, and you can make it work with minimal components and next to no calculations. Hopefully you were able to at-least negotiate the price down - given the condition, I myself would offer less than $100 for it, especially since the shipping is so high as well. Again, for my goals I may not get the same pump, but for you it could work perfectly (assuming the heater is ok).