Can I do the intention of fasting after fajr if I haven't eaten anything? Also can one combine the intentions, for example combining fasting for lust, old Ramadan fasts, fast of sha'aban, the fast of Monday and Tuesday and the fast of dawud?

Ustadh AbdulAziz al-Haqqan

Only voluntary fasting as for making up and obligatory one, no it has to be before fajr.