I keep my lights active 12 hours a day with a ramp up and down of about 1 1/2 hrs dusk /dawn. Not sure if your lights have that programability or not. Others have different schedules depending on preference and livestock considerations. As for the tests, let's start with the basics for now. Salinity is ok for time being as you take it from ocean, although I would assume you still have to top off with RODI water between changes? Somebody else can advise on this as I don't honestly know...
Nitrate, Phosphate, are the two basic big ones IMO. Your test strips likely give you Nitrate readings but are wildly inaccurate. I would recommend hitting your LFS and inquiring about a basic marine test kit, or simply purchase one of each for Nitrate and Phosphate. They will come with reagents to add to the test vial and you can compare numbers on a colour chart in many cases. Salifert is one they likely have, I prefer the Nyos brand. Really at the end of the day, you just need some simple testing done to point at potential problems. Later on you down the road you could invest in other testing for Alk, Calcium etc...
As for what your levels 'should be at ' you'll get different viewpoints as well. I like my Nitrates a bit lower around 5ppm and Phos below .15, others will have different opinions.