Networks

The need for a distinction between crossover cables or straight through cables is not critical as it was in times past. Most all modern day routers and switches are auto-sensing, meaning they will automatically set the port properly irrespective of which of the two types of cabling used.

Your proposed scheme of hooking the devices up is correct.

Yes, it will work. New routers and switches no longer have uplink ports because all of the ports are auto-sensing and configure themselves automatically; no special cables needed.

You could put the router before or after the switch. You could use the WAN port or a "regular" port off of the router. All of these configurations will "work" but they will have different potential effects.

If you wanted to put your wireless clients on a separate subnet from your other switch ports you would put the switch first and then connect a switch port to your router using the WAN port on the router. If you want to use the DHCP on your AP for both wired and wireless clients then you would put the router first, WAN port facing the WAN and a regular port to the switch.