P.S. I only mention parts which haven't mentioned by other member.
- Why do we need to run Bitcoin full node or EPS (Electrum Personal Server) to provide full anonymity. How is it any different from using Trezor with Tor browser, or using Trezor with Electrum running on Tor?
To avoid the possibility server log set of your addresses, which can be used to trace you. Your anonymity could gone completely even if one address is linked with your identity.
- If this is the case with Bitcoin where I have to run Bitcoin full node or EPS to achieve full anonymity, does this apply to Ethereum as well and I have to run Ethereum full node, or it is sufficient to use TOR browser when receiving or sending ETH?
Yes, it applies to all cryptocurrency.
- Do I need to worry about Xpub being transmitted any time when making transactions or just making sure during initialising it for the first time it does not get leaked?
Usually wallet software don't transmit your xpub, but only set of generated address to obtain transaction history.