Learn Polish: Nie mam wątpliwości, że on mówi prawdę. - I have no doubt that he is telling the truth.

The verb mieć (to have) normally takes the accusative case, but here it is negated (nie mam). In Polish, a negated direct object always takes the genitive case. For feminine nouns ending in a consonant like -ść, the genitive ending is -i.

Is wątpliwości singular or plural in this sentence?

It can be either! For feminine nouns ending in -ść, the genitive singular and the genitive plural are identical (wątpliwości). So this sentence translates equally well to "I have no doubt" and "I have no doubts".

Why is there a comma before że?

In Polish punctuation, you must always put a comma before the conjunction że (that) when it connects two parts of a sentence. English often drops the comma or the word "that" entirely, but Polish requires both.

Could I leave out the word on?

Yes, you could just say że mówi prawdę. Including on (he) isn't strictly necessary because the verb form mówi already shows it is third-person singular. Using on here just adds a little emphasis, or clarifies who you mean if multiple people were mentioned.