You can access the Web Chat client by clicking here or going to https://wc2.tochat.org/

Common browsers like Safari, Google Chrome, Firefox and Microsoft Edge support chat.
Basically any browser that supports HTML5.

When you close Web Chat your connection to chat will be closed and users will see you sign out (QUIT).
Your session is only active as long as you have the tab/browser open.

Yes however you're limited to 3 concurrent connections to the server.
If you exceed the limit you may be disconnected from the server until the count drops.
If the server doesn't receive regular responses from you (automatic) it will disconnect "Ping Timeout" your connection.

You have two options. You can use the GUI and click on the user's name on right panel and change the user's status (to Voice, Op, etc.) depending your level in chat.
You can also use /mode <#channel> +o to op.
You can also use /mode <#channel> +v to voice.
You can replace a (+) with a (-) to remove op or voice from the user.

Depending on the symbol preceding their name indicates that person's access level in the channel.
Below are what each Symbol means
(Replace NICK with the chatter's nick)

List is from least permissions to most
NICK = Regular chat user
+NICK = Voiced User (Allows ability to chat in moderated rooms)
%NICK = Half-Op User (Allows minimal ability to manage room. Change topic, kick regular or voiced users).
@NICK = Operator/Op User (Allows all channel management but cannot manage users above Op)
&NICK = Channel Administrator (Allows all channel management but cannot manage channel founder/owners.
~NICK = Channel Founder/Owners (Allows all channel management for all channel users).

Half-op and above are considered Channel staff. (Does not mean TO Chat Staff)

This is a very simple process.
Depending on how you want to do it (IE iframe, etc.) you just link to https://wc2.tochat.org/<#channel>
Replacing <#channel> with your channel. IE: https://wc2.tochat.org/#Lobby

When connected to chat click on your Initial in the circle above TO Chat.
You will then see an option below it to "Forget Me".
Confirm then reload the page.
Your settings will now be back to default.

Alternatively any time you clear your temporary internet files and cookies the settings will be cleared then as well.

Yes it does!
Simply access it via the same URL. https://wc2.tochat.org
It will run in the mobile version for you!