I will cautiously answer the first part of your question as the evidence about reactivation of lupus nephritis or systemic manifestations is limited to case reports or series.
However I was able to find a paper that followed 97 patients and found that a minimal number of patients had reactivation of disease after receiving a renal transplant.
(REF: Arthritis Rheum. 1998 Apr;41(4):678-86.
Renal transplants are associated with immunosuppression and, as a result, autoimmune diseases are also suppressed (like SLE). There has been documented evidence of reactivation of lupus-like manifestations in HIV patients when they are started in HAART (because of an improvement in immunity.
(REF: J Clin Rheumatol. 2003 Jun;9(3):176-80.
I was lucky enough to attend a grand rounds presentation by a resident interested in rheumatology about reactivation of Lupus and other autoimmune disease in patients with renal transplant (I am trying to get in touch with that physician to see if I can find the references used in that presentation). The inference of that talk was that during the phase when immunosuppression is held or reduced (due to instances like infection), the chances of lupus reactivation of increases.
Regarding the second part of your question: you are right about the classes of Lupus Nephritis findings on renal biopsy.
The treatment differs slightly with the severity of disease. The mainstay of treatment is Cyclophosphamide/Myfortic or less likely prograf for induction and same for maintainance with steroids during induction phase and maintainance if cyclophosphamide is used.
Remission means there is no active disease activity suggested by urine markers, systemic disease activity, and worsening renal function.
During remission, antibody production is either quiesant or suppressed by medications. The renal manifestations do not completely reverse but a substantial improvement would be noted if biopsy is done at that time. Again, remission usually is judged by clincal manifestation rather than subjecting a patient to biopsy.