Can I bleed after giving myself a fleet?

Possible... Inserting a fleet up can cause irritation/breaking of the internal blood vessels--hemorrhoids-and thus can cause some bleeding etc..Make sure that the fleet caplet is nicely coated/wet/slippery and insert it gently and slowly to avoid injurying the local tissue/vessels etc... Regular use of fibers and increase fluid can reduce need for fleet use..Consult your doc...Good luck.
Yes. Usually traumatic, but if persists, see a olon and rectal surgeon.
Possibly. If the enema tip was not lubricated properly, or if you have a fissure or internal hemorrhoids you could bleed. Less frequently you could see bleeing if you have rectal inflammation such as proctitis or if you have a polyp/tumor of the lower colon. No amount of bleeding is normal. See a GI or colorectal surgeon and get a proper evaluation.