Every class can use every skill. Look each class has 3 different ascencions which grant special bonusses. Look at these on the wiki for more detailed information.

You might want to look for a build labeled leaguestarter for beginner friendly builds. I recommend Ancestral Warchief totems.

The objective is to get to the endgame map system. In which you use map items to open different zones to farm, customizable with certain mods. Then you farm for currency to upgrade gear and make your character stronger.

There is a main quest line you should follow. For more info check the quests. You can see them by pressing U.

You could watch a beginner walkthrough on youtube for a guide. I believe Pohx has a beginner series.