You can sue anyone, anytime, for anything, but even if charges aren't filed or a court dismisses them at the preliminary hearing stage for lack of sufficient evidence, wrongful arrest suits against police are very difficult.
No, mere suspicion is not sufficient for arrest.
> "Probable cause" relates to searching or entering private property.
It also relates to arrest. The Fourth Amendment provision applying the standard explicitly applies to searches and seizures of persons, houses, and effects. Arrest is seizure of one’s person.
A drug dog’s indications provide probable cause for searching your car, but are not enough to arrest you.
Probable cause (of slightly different things; the threshold is the same but the subject is different) is the bar for both search and arrest.