Is absence from Fajr prayer considered a sin despite trying to wake up, and does committing sins prevent one from waking up for it?

Congratulations on your eagerness to perform the prayer in congregation. There is no sin upon you if you slept before Fajr while being keen on it, and then missed it. What is necessary is to strive to adopt all means that aid in waking up, such as entrusting someone to wake you, which might be the best method after the alarm fails. You are not obligated to exercise or take any specific measure to wake up for Fajr prayer in congregation. The ill effects of sins might result in missing some acts of obedience. If you commit sins, that could be a reason for your deprivation from Fajr prayer in congregation, because sins harden the heart and stand between it and the means of mercy.