I’m not affiliated with a church, or even a religion anymore, and I still ‘literally pray for people’, yes.
Same here. And I’m a little uncomfortable when someone specifically says, “please, keep me in your prayers”. I don’t want to explain that I don’t do praying, I don’t want to tell them, “no”, and so I just kind of do a sage head nod and walk away.
I’ll say at least a quick prayer for the person in these situations. So, yes, I mean it literally, albeit not in the sense of a full novena.
Word-for-word, this is my experience and view, as well.
I’d assume they mean it literally,
I don’t recall anyone ever saying it to me and not sure how I’d feel about it. I think I find it rather off-putting to be honest. I mean I definitely don’t want anyone saying prayers for me but how could I tell them not to?
Do you end your prayers with “regards, Shodan”? 
There have been times when I said I would and then forgot to; I felt incredibly guilty. I go back and forth about whether I believe God intervenes in any way. But no matter where I am immediately in the pendulum swing, if they believe, and it will be a comfort to them, I’m always willing to spend 2 minutes on my knees for them. Sometimes I feel ridiculous doing it, and other times it feels like a very powerful force for good.
Amen,
Shodan