As long as you can access the router you can use Webfig (and terminal) or SSH just fine.
The advantage of Winbox is (among a few minor ones) that it can normally connect to a Mikrotik device both via its IP address and via its MAC address, this latter feature allows for connecting to the router in most of the common cases where a “wrong” setting prevents communication via the IP address (layer3), which - unfortunately it is common enough when fiddling with settings.
Since you are a Linux guy, you shouldn’t have any issues using Mikrotik’s terminal which is very similar to common Linux (or DOS-like) command line.
But even if it bothers you, you should take the time to have Winbox (under Wine) running and working BEFORE disaster happens and you get locked out, it may never happen, still …
Think of the whole stuff as you think of your home door lock, is it better to spend an hour to go to the locksmith and have a copy of your key made (that you will store in some safe place and hopefully never use) or wait until you are locked out at night and need to call some emergency service to enter your home?
Now, the procedure you described is more or less correct, you might still have some unwanted remains (that shouldn’t affect the way the device should work as switch/AP), and no, there is no difference in rebooting initiating the reboot via software vs initiating it by pulling the plug (the latter will create a different log entry, but that’s it).
Compare with this recent, essentially similar, thread:
http://forum.mikrotik.com/t/can-a-powerbox-rb750p-pbr-2-do-this/177353/1
What might be missing is some mechanism giving out the DHCP addresses coming from your AT&T router or some other (needed) “hooking” of the wi-fi interface(s).
You should follow this post (using Webfig instead of Winbox the procedure should be very similar):
http://forum.mikrotik.com/t/forum-rules/173010/1
and provide your configuration export, so that some willing to help member may point out the issues or omissions.
About firewall, the normally most used chain (forward) is unused when the device is configured as switch (so you can disable or remove those rules), but you may want to keep (modifying them in a suitable way) the rules in the input chain to limit and protect access to the device.
As anav just suggested, if you don’t need all the ports, it would be a good idea to keep a port off the bridge for emergency access only.