First Question. Can you explain "if (!client.connected()) {
client.stop();" as used in the above code please. Won't it miss out the next part
All I can deduce from the code is that the ethernet library has a function, client.connected(), which will respond true/not true if a connection is made to a server. Putting in the ! turns it into NOT connected. If there is no connection the server, then the code starts doing other things.
Shouldn't I be able to type Code:http://192.168.1.19/<heater1=on>
and hit Enter to turn the LED on?
No for a couple of reasons. First is that the url is not made to http get standards. There is no ? to indicate an attached query_string, and the <> characters may be reserved and probably can't be used in a query_string. Second, it appears that you are trying to send a client request to an arduino client. Clients do not receive request, they send request to servers. Servers receive request from clients and return info to the client. Servers do not send request. Using google, search for things like "http tutorial", "query_string tutorial", "http get" and "http post", and similar to get familiar with what you are working with.