Learn Russian: Никто не знает, спросит ли таможня про этот сертификат. - Nobody knows whether customs will ask about this certificate.

In Russian, the particle ли always directly follows the word that is the main focus of the question. Because the uncertainty is specifically whether they will ask or not, the verb спросит is placed first in the clause, immediately followed by ли.

Could I change the word order and say таможня ли спросит instead?

You could, but it changes the meaning! Placing ли after таможня emphasizes the customs office: 'Nobody knows whether it is customs (or some other agency) that will ask...' Since we just want to know if the action of asking will happen, the verb goes first.

Why does the sentence use про этот сертификат instead of об этом сертификате?

Both mean 'about this certificate', but the preposition про (which takes the accusative case) is very common in everyday, conversational Russian. Using о or об (which takes the prepositional case) is slightly more formal but would also be perfectly correct here.

Why is there a не before знает if the sentence already starts with Никто (Nobody)?