Why do I get warnings for all my voltage supply connections in Eagle CAD?
This is a stupidity of Eagle.  Unfortunately you get these warnings when a supply pin is connected to a net with a different name than the pin.

Even worse, Eagle will implicitly connect a supply pin to a net of the same name.  I and many other people, judging from the Cadsoft forums, think this is stupid too, but Cadsoft has so far refused to fix this.

Don't get the overall wrong impression of Eagle.  It's a great package offered at a great price, and that's what I use too.  Like any complicated piece of software, it has its quirks and some downright dumb choices.

A few other things to get used to: Lines are drawn with the WIRE command, except when they represent wires, then you use the NET command.  CUT doesn't do a cut, but a copy, and COPY never seems to do anything useful.