The species is Leptospira interrogans & the 3 serovars most commonly infecting dogs are icterohaemorrhagiae, gripptyphosa, & canicola
Yes, Lepto can be transmitted by bite wound. It can also be transmitted by eating an infected animal. It also can be transmitted from fomites.
Recovered dogs shed organism for months to years.
Yes, freezing will kill leptospires.
This is the traditional test for determining titer. Take some cultured leptospires & expose them to varying dilutions of patient serum. The endpoint is the dilution that agglutinates 50% of the organisms. (You need darkfield microscopy to do this test.) You may need to show a 4 fold increase in titer over 2-4 weeks for diagnosis as titer is frequently negative by this method in the first week. There is currently an IgM detecting ELISA which is more sensitive.
Leptospires have fastidious culture requirements & are quickly over grown as the conventional bacterial proliferate post-mortem.