First, you might try clearing your cache. I use Firefox a lot and haven't seen issues with sending messages. Don't receive many challenges or requests so can't speak to the current state.
I'm not on an Apple product either. One other thing to check, is to see if the browser is trying to use hardware acceleration and turn that off.
V3 can't send messages, accept challengs or friend requests
This is, to put it mildly, a showtopper. I'm sure it's a temporary regression, but I'm back on V2 until someone assures me that V3 actually works.
Right now, it's in a state of flux, and if most but not all changes are provements, it is still *slow* *slow* *slow* on Firefox on OS X.
Not to mention I can't access chess.com using Google's Chrome, but it picks up all sorts of defaults so "who knows."
I am not willing to use Safari. Full stop, period. I hate to consider leaving chess.com or dropping any form of paid membership, but V3 had better pick up very fast or when my membership is due for rewnewl ... bye bye.
I'll note that some combination of Firefox and OS X El Capitan is hitting some single threaded limit in the OS. I am very tired of seeing OS X's beachball when I open multiple games in multiple tabs.
Chess.com is good but not perfect. V3 varies between "slow, but I like it" and utterly ususable.
There are other chess sites on the Internet.
Sorry this is so negative, but tomorrow I'm going to start trying one or two of those other sites.
Not being able to communicate wth other members makes the sites a total loss. :-(
ollave, aka Giles Lean.