Prayers are not accepted if they are performed early. It is better to pray soon after the prescribed time starts, but you have until the time of the next prayer to complete it. The accepted time for the Fajr prayer ends at Shurooq time. You are not supposed to pray optional prayers soon after sunrise or between Asr and Mahgrib time. If you are travelling, you can shorten the Dhuhr, Asr, and Ishaa prayers to 2 rakat and you can combine Dhuhr with Asr and Mahgrib with Ishaa. There are recommended optional prayers that can also be performed at certain times, that information can be found online, but I have only covered what is obligatory.
Salaat Time is a freeware program for telling you the prayer times for your location. You can either choose the city you live in, or if you want to be very accurate you can look up the exact longitude/latitude of your location and enter it that way. You can customize it to either do an athan, or alert you in other ways. I do not use a smartphone, so maybe someone could recommend a good prayer time app for phones.
https://www.salaattime.com/salaat-time/
