Just like the verb être (to be), avoir (to have) is an irregular verb.
Its forms are easiest learned individually. So watch out when using it.
on is a general way to address a group of people and nobody in particular. We could translate it in English as one: "One always has time to drink tea!"
You sound like the queen...
Yes, it sounds silly in English, but it's not so bad in French. We'll get to that later though.
Here's a quick review of both verbs:
il, elle, on
The verb avoir is also used to form many common expressions:
to be cold ⇒ to have cold
to be hot ⇒ to have hot
to be thirsty ⇒ to have thirsty
to be hungry ⇒ to have hungry
Cool, but do I need to know all of these?
Oh no, of course not, but it helps to be aware of this. You'll learn these and more expressions as you go along!
I'll focus on getting avoir and être right first...