Learn Italian: L'uomo sospettoso non vuole fare il giuramento senza di noi. - The suspicious man does not want to take the oath without us.

When certain prepositions like senza (without), dopo (after), contro (against), sopra (above), and sotto (under) are followed directly by a personal pronoun (like noi, me, te), Italian requires you to insert di between them. So, while you would say senza l'uomo (without the man), you must say senza di noi (without us).

What is the difference between sospettoso and sospetto? Could I use l'uomo sospetto here?

They mean two different things! Sospettoso describes someone who feels suspicious or distrustful of others, which fits this sentence perfectly since he is refusing to take the oath without you. Sospetto, on the other hand, describes someone who arouses suspicion (a shady or suspicious-looking person), or it acts as a noun meaning 'the suspect'.

The English translation says 'to take the oath', but the Italian uses fare. Can I use prendere here?

No, prendere il giuramento would sound unnatural. In Italian, collocations (words that naturally go together) often differ from English. You 'make' or 'do' an oath (fare un giuramento), or you simply use the verb giurare (to swear).