Any process that you would need to use the NuArc for can be done in a dimroom... no daylight or fluorescent lights. Incandescent or LED lighting is OK... it doesn't even have to be particularly dim.
You can probably use the unit without the vacuum for small negatives, you would probably want to arrange some weights (a few heavy books should suffice) on top of the negative/paper sandwich if you don't use the vacuum. This is all about maintaining tight contact between the paper and negative during the exposure.
As for pump oil, Google "vacuum pump oil". This is pretty generic. Most simple mechanical vacuum pumps use a specially purified grade of mineral oil, but which supplier is used probably does not matter as long as it is specified for use in mechanical vacuum pumps.
Depending on where you are planning to use the NuArc consider getting a oil mist filter for the output of the vacuum pump if it is not already equipped with one. I would also take care to maintain this filter regularly.
All mechanical pumps that use oil, put out a little oil in the output air by design. This is why one need to replenish the oil periodically. Thus I would probably not use the pump without a mist filter in a home environment.
Lastly, I would, if possible, put it in the different space from optics optics that I wanted to keep pristine. This is less critical than the mist filter.
In my view, the only reason to use a NuArc is if you want to make large prints (say larger than 11x14 inches). Otherwise, a homemade exposure unit using blacklight LEDs and a contact printing frame is much more convenient and gives good results.