The "deadtalk" setting should prevent eliminated players from communicating with live players, but it's a server side setting. Eliminated players can still communicate with each other as well.
"P" is the default key to chase players, "[" and "]" are the default keys to switch players.
You might be scrolled up too far if your console is blank. Try hitting CTRL+END to get to the most current console data.
Like any game, there are griefers. I've thought about a push command, but it could be worse than not having it. People might go around shoving people out from cover, off of cliffs, etc. As for smoke grenades, most people don't bother learning that there's a "dropgren" bind that can be used to drop a smoke grenade when they want to pick up a paint grenade instead, so they just use the "tossgren" to throw smoke grenades in their teammate's faces.