I'm usually friendly to strangers but I'd be immediately suspicious of someone asking me either of these questions out of the blue - and I'm a middle class, middle aged male.
It might be a cultural thing but yes, here in Europe I would be pretty suspicious of someone approaching me like that out of the blue. I mean, heck, that's none of your business!?
That's fine. Not every conversation turns into friendship.
Most of mine I am trying to find similarities or learn new things.
After the conversation is over, it won't matter how you opened, it won't matter if the person felt suspicious. I can't control your upbringing or your day.
You either are friends, or you likely won't see them again.