The usage of Ethercard.h instead of Ethernet.h is what is causing the problems.
Client.read does not exist and I can't figure out how to put the buffer into a char instead of just getting printed.
No, the use of Ethercard is NOT causing your problem. Your refusal to look at the code and understand what it is doing is.
In my_result_cb(), you have a statement that prints the whole packet returned by the GET request, as a NULL terminated array of char, There are string functions that let you find stuff in that array, just like TextFinder does. If you want to parse that data, strtok() could be used to get each line, delimited by CR or LF.
You still haven't told us of you have any control over the website you are accessing, or whether you could change the output to make parsing it easier.