How can i play a cup? And how can i know when the cup begins?

of course yes...
you can play in a cup that suitable to your level...

there is many cup tournament in some time interval, so you just select a cup and wait till the time limit...

you know when the cup begin when you see your enemy team at left panel and link to setting your formation

or, if the time limit past about 2 minutes, it mean you didnt choosen to that cup, so yo have to join another tournament