Stawia comes from stawiać.
In On stawia sobie cel, stawia is:
So it can mean things like:
Which English version fits best depends on context.
Cel is the direct object of stawia, so it is in the accusative case.
But cel is a masculine inanimate noun, and in the singular, the accusative often looks exactly the same as the nominative.
So:
That is why you do not see a different ending here.
Yes. It is a normal and natural expression meaning to set oneself a goal.
You may also hear related phrases like:
They are similar, though the aspect and nuance can differ a bit.
Yes, on can often be omitted.
Polish frequently leaves out subject pronouns when the subject is clear from context. So you can say:
However, on may be included for:
Also, stawia by itself could mean he/she/it sets, so on makes it explicit that the subject is he.
It can mean either, depending on context.
Because stawiać is imperfective, the present tense in Polish can express:
Context tells you which reading is intended.
The perfective partner is usually postawić.
So you get a contrast like this:
For example:
Yes. Polish word order is more flexible than English word order.
You may hear:
These versions are not all equally neutral, but they are possible. The differences are mainly about emphasis and information focus, not basic meaning.
The given sentence is a normal, neutral order.
It can mean all of those, depending on context.
Most naturally here, cel means:
In other situations, it can also mean target.
So in this sentence, the most idiomatic English meaning is usually goal.
Because Polish does not have articles like English a/an and the.
So cel can mean:
The exact meaning depends on context. In an isolated sentence like this, English usually translates it as a goal.
The singular is completely natural if you mean one specific goal.
The plural is also common in other contexts:
So:
Both are natural; they just mean different things.