I recall both ident and addhost being disabled (unbound) by default in recent eggdrops. Have you checked that these are not disabled?
When using the .+host, did you take into account the strict-hosts setting (if applicable)?
If possible, gain access to the partyline (possibly through telnet), and connect your irc client using your vhost. Then use the .channels partyline command to give you a "bot's view" of the channel - what nick, user@host the bot sees; which, if any user record it recognizes any channel member as, and a few other interresting pieces of information.
That information tells me your eggdrop recognizes you perfectly fine when using the Vhost. The CHAT ctcp-message requres the ctcp-module to be loaded and a listen-port to be enabled. There might be some issues trying to use /dcc chat requests, as your eggdrop might find that your hostname does not match the IP sent to it in the chat request, and thus considers the request invalid or bogus.
I'm not sure why it ignores MSG commands though. A first thought would be to check your eggdrop's ignore-list if you have not already done this (.ignores from the dcc chat partyline)