I will graduate in December of 2016. I am applying for TPS but have no problem maintaining F1 status till then. I am wondering if it is the only time to apply for EAD or its possible to apply for it later when needed (lets say after my OPT expires and I didn't get H1B by then if TPS continues till that period). Will working on TPS EAD create any issue when applying for H1B through employment?

On different note, can all Nepalese working on TPS EAD apply for H1B in future if their employer agrees to do so?