Wikipedia is your friend (see the article below and its references).
In brief: Uracil is removed from the DNA by (at least) two mechanisms (UNG or MSH2/MSH6 dependent), which ultimately leads in the excision of a short strech of the U-containing strand. The resulting gap is filled up by patch polymerases that have a high error rate and will therefore cause mutations other than the initial C-to-U transition.
BCR-dependent activation of the cell is a requirement for the induction of SHM, however it is not sufficient. AID activation is potentially detrimental and therefore tightly regulated, and I am not sure whether the downstream signaling cascade leading to AID activation is currently fully understood. SHM usually only occurs in the germinal center and requires additional signaling from T cells. CSR is not strictly T dependent, but T cell signaling nevertheless has a strong positive effect on switching. Finally, since AID only acts on ssDNA, the target loci have to be transcriptionally active, which is another layer of regulation.