How do I know if the uv lights are O.K.
Will I see the lights glow when the lights are powered up?
You buy new bulbs. It's the only option unless you trust the previous owner estimates. UV bulbs continue to light up emitting visible light but lose UV strength over time.
Another choice is to hook them up and watch the water. If the pond water starts to turn green the UV is not working. Whether the problem is the bulbs or the install is another matter. A properly installed and maintained UV is 100% effective in kill green water algae in 3-5 days when water was already green. In a new pond the water should never turn green. However there are edge conditions like a new pond's bloom being so strong the UV can't keep up but will after awhile. That kind of stuff.
Before buying bulbs I would confirm the UV you have is the right size for your pond and pump. Too small a UV won't keep a pond clear even with new bulbs. A pump pushing water thru the UV too fast won't keep a pond clear. You can trust the previous owner and roll the dice, or check the specs.
It came with 2 in the skimmer and the owner tells me the filter motor needs to run with the lights. I plan on hooking the filter pump and UV lights on a timer together.
Like Sissy said, UV must normally run 24/7 because it's sized to a pond. There are exceptions, like an oversized UV and pump, or a light algae bloom, etc.
Always a good idea having both on the same circuit and/or timer. Otherwise the pump circuit can trip causing the UV to overheat.
Pumps can be on timers. Depends on fish load, water temp, and many other factors. Many ponds can run without any pump at all. But the UV requires water flow to stay cool.
Often a pond will stay clear without a UV after the UV has killed all the green water algae. There are a few theories as why this happens. Mine is the lack of green water algae allows other algae to grow, macro algae, like what is probably on your pond liner. The macro algae produce a chemical killing the green water algae. Whatever keeps the water clear one thing that is known is that something is created in the water that kills the green water algae. This has been confirmed by pouring water from a clear pond into a container of water from a green pond. The green water algae are killed very fast and in proportion to the amount of clear water added.
So, if you choose you could install the liner the same way as in the previous pond. That might give the macro algae the jump and could clear your pond pretty fast without any UV. Macro algae will find its way into your pond regardless of which way the liner is installed. Macro algae can be it's own problem but that can't really be stopped without chemicals that hurt fish.