Can I alternate between server and client using an ESP8266Wifi for the networking device?

Which ESP8266 firmware do you have? 0.25?

It looks to me like the ESP8266 driver isn't actually closing the server when you say close... So it's possible the page is wrong and you actually can do TCP/IP requests while having a server. Might be worth a try?

But I'll have to fix the driver so that it properly closes the server. A hack for now would be (I think):

wifi.at.cmd("AT+CIPSERVER=0\r\n",1000,print);