The conversion doesn't care if it is raining or not, but you might. If you feel like continuing in the rain, that is fine. If you want to take a break, that is also fine.
FC is free chlorine, active chlorine available to sanitize the pool or perform the conversion
CC is combined chlorine, an inactive form of chlorine that appears temporarily when the chlorine is working. Normally, you don't want any CC in the pool.
TC is total chlorine, the sum of FC and CC.
During a baquacil conversion the CC level can get quite high. As chlorine works, it first forms CC fairly quickly, and then breaks down further at a much slower rate. Doing a conversion, there is so much work for the chlorine to do that a lot of CC gets formed and takes a long time to break down. You will know when the conversion is finally over when the CC level finally goes down.
Doing the FAS-DPD test when there is a high CC level can cause the sample to turn pink again quite quickly after it goes clear. You want to add drops till it turns clear and stays clear for several seconds. If you then leave the sample alone for just a little longer it will turn pink again, which isn't a problem and does not count.