It sounds like your LFS is just throwing out ideas without any evidence to back them up. That's no way to give reef tank advice.
Regarding testing, look up one of the mail-in tests like Triton. They test for all sorts of things including toxic metals (eg from internal pump corrosion) that you can't test for otherwise. Many of us do one of these tests yearly these days both to check for weird stuff and also double-check our standard testing regimens. Plus the tests are cheap enough that I do one whenever I'm at wits end with a problem. For regular testing, I'd suggest that you do your own testing instead of using the LFS. If money isn't tight, get Hanna checkers for Ca, Alk, Phosphorus ULR (HI736, not Phosphate---see threads
@Randy Holmes-Farley and while you're at it, see his thread on optimal parameters), and Nitrate LR. If money is tight, get Salifert or Red Sea tests. For Magnesium, I think most of us use Salifert or Red Sea, but if you find a better one please let me know as I think both have accuracy issues. Don't use API for anything except emergency ammonia testing. I assume you're already testing for pH and salinity on your own? Make sure any probes you're using are calibrated correctly including for temperature correction (the Apex salinity probe calibration is tricky---see
@eag). In addition to watching temp, salinity, and pH every day, I'd also check Alk every day. It's important to keep all of these relatively stable. Just try to check these at the same time every day ideally during the middle of your peak light cycle. Test the others once a week before you do any water change.
For lighting, you can rent a PAR meter from BRS for pretty cheap and test all over your tank for light levels. That's what I'd recommend. You can also buy a meter or even a sensor that you can use with your computer or phone. My guess, like
@monkeyCmonkeyDo, is that your tank is too dark, but I don't want to base a recommendation off of a photo. Leave the lighting alone until you can do PAR measurements.
For coral nutrition, reef roids is a good choice. I'd also recommend daily or every-other day dosing of Red Sea Reef Energy AB+. Just make sure you follow the directions and don't overdose it. Also, look into a trace element supplement---all the good brands produce one. (The mail-in test will give you a report on trace elements too.)
Overall, it sounds to me like you need to spend time collecting evidence before you try changing anything. Remember that nothing good happens fast in a reef tank---and the corollary that doing anything half-cocked in a reef tank is a recipe for heartbreak. Luckily, it doesn't look like you're in an emergency situation so you have time to figure things out. Sorry if I'm coming off sounding preachy---not my intent. It's early on Sunday morning and my coffee hasn't kicked in yet. Good luck and have fun!
