Hey Lnphappy, I recommend the tuning app “INSTunerLite.” I like this app as it turns different colors as when you are on different pitches. Green indicates “in tune,” and red indicates “out of tune.” This app is great but I believe only available on Apple devices. Regarding other apps, I’ve really have never seen one I’ve been disappointed with. Download one that is most popular with the best ratings.
Regarding your question about the screw (fine tuners). These can only be twisted so far (in either direction), so once you reach the top or the bottom, you should adjust the fine tuner back to “normal” position, and then compensate (tune) with the peg. When I say “normal” position with the fine tuner, this means a spot where you have room to twist in either direction without running out of space.
Great questions! For those of you that need help with tuning, check out my tuning video.