Spectator mode

#1 You can add the following to the player datablock to force observing in first person

observeThroughObject = true;

#2 Item #2, sounds like you could just disable the chat hud stuff until the player respawns.

something.visible=false;

[Edit: fixed syntax problem]

#3 For disabeling chat i would go with letting the server filter messages to dead and living players. There is already a method to exclude a client from a message (used in gameConnection::onConnect).

#4 The message functions are in common/message.cs

As you've asked to disable chat in a specific gametype, it makes things a little more complicated. You'll need to hook the gametype scripting (if you use gametype scripting) into the message scripting to give it the go-ahead to push the message to the clients. If you dont use gametype scripting, you can simply do the checks in the functions below.
If you've not changed much from the default scripting, the two functions you want to use are chatMessageTeam() and chatMessageAll() found at the bottom of the script above. They are the functions used to send team and global messages by default.
The check you will probably want to do is:

if(isObject(%sender.player) && %sender.player.getState() $= "Dead")
    continue;

That code would go in the for cycle, and will skip any dead players.

#5 Wow excellent responses. Thank you to all.