DHCP is the method by which your phone is assigned an IP address whenever you connect to a wireless network, exactly as in the scenario you mention. Basically (and oversimplified) when you connect to the network, you announce to everyone "Everybody, I'm here on this network now! Hey router, I'm a phone with the MAC address of 00:01:02:03:04 (or whatever) Can you give me an IP to use?" And the router responds "Yes phone 00:01:02:03:04, for this connection you should use the IP of 192.168.1.105" and from then on that's your IP.
If you're deleting files and folders out of
/data/misc/dhcp, you're removing the place that the wifi system sets and stores wifi/network-related information, so I'm not surprised that you'd be having issues. In fact, sometimes just doing a
rm -rf /data/misc/wifi can solve some corrupted/messed up wifi issues, but of course you lose all your settings when they are re-created. At reboot, those folders are usually recreated if they are missing and their permissions and ownership is adjusted, but if you're asking if deleting stuff in there is related, then the answer is probably yes, depending on when and how often you're clearing it out. A reboot when you're near one of these open wifis may help if you've messed with those directories since rebooting.
One final observation is that there appears to be a cm10 for your device. If you're still on cm9, you may want to upgrade.