Use the hotkeys. You don't need to 'learn' them, just use them and after a while you will just start doing it automatically.
My left hand generally sits with my index finger on the B key. Most of the common build commands are easily accessable to the left of there... BB BF BT BS etc. just BL for a mill where you have to use the right hand side of your keyboard for the basic stuff, and later there's VI (inventor) and VO (ogre mound). By the time you're building alter,mage tower, etc you can afford an extra second or two to find the key or use the mouse.
*Best tip for WC2* When you build your hall, select it and press CTRL-0 (that's CTRL-Zero)
*Then to build a peon just press 0P ([zero] - [P]) Zero will select your hall, the P trains a peasant/peon.
*Just get into the habit of pressing 0P every time you hear "ready to serve".
Later when you have a few barracks built, use the hotkeys to train. i.e. if you're sending knights, just have your finger on the [K] key then just click on each barracks with the mouse and press K.
... and in answer to the subject line question: NO - you don't have to beat comps, you're supposed to beat other players
If you have no idea about how to beat a comp, then you have little chance of beating a human player, that being said, you don't necessarily have to be able to beat all comps on all maps. As you are discovering, some of them are much harder than others.
Ultimately there is no way to get good at beating other players other than playing against other players. You should play vs comps to learn the basics and get an idea of what you're doing - like the order you usually build things in, which buildings train which units, and which buildings are prerequsites for building others etc.
Personally I can't recall ever having tried to play vs comps on GSEW so don't sweat individual maps, and just be prepared to lose vs other players a bit until you get up to speed. Mainly just have fun, LISTEN to more experienced players who are trying to help, and ignore the handfull of dicks who will say dickish things because you're new (sorry about them, but remember they're fat losers with no life and just say GG).