If there is a branch at CW you simply take your book in and ask the teller for an update. This will make a B/F entry in your book. But yes, making a deposit or withdrawal will have the same effect
Agent doesn't help. Sadly some expats living in Thailand think it's the same as using a visa agent to get a Thai visa, where a bribe is paid to an immigration officer. Doesn't work that way with UK visa. All UK visas are processed through a separate department at the British embassy in India. Good luck reaching them!
It's easy. Do the application online through the embassy, answer every question, attach relevant documents, then she attends VFS (currently in Soi 13, but I think they're moving soon) to do biometrics. Pay the dosh and you're laughing