[KCD1] Random Encounters?

I finished the second game just in time for the first one to update for the Xbox, so I started playing the original. I'm noticing a lack of random encounter missions. So far, just ambushes and maybe a beggar selling savior schnapps.

Are there more one-off encounters like the second game? Like dueling a noble, meeting cumans, finding a moneylending Jew who sells bagels, a schizo with religious relics, convincing a guy to dress up as a nun, etc. It seems to be lacking.

Do they only trigger in fast travel?