If you use anti-rabbit antibodies in a rabbit model, you have to worry about endogenous antibodies which might produce a spurious signal. Whether this is a problem would depend on the specific experiments you are performing. You 'd definitely have to be extra diligent about negative controls to ensure you have no false positives due to contamination with endogenous rabbit antibodies.
I don't understand your question. Can you offer more details?
Are you trying a passive immunization with a specific Ab from rabbit in the same specie? If yes, I agree with Annemarie. Negative control will be very important in the assay because endogenous Ab response could cause false positive results.
Of course, the nature of the antigen is very important too. If you are are working with an Ag with very high specific epitopes maybe you can obtain good results even when you test low dilution of negative rabbit serum.