This isn't a question of correctness, as I already know the answer, but more one of tendency. How likely are you, in casual speech, to replace the infinitive verb indicator to with and? Try and keep that in mind. Try to keep that in mind. What's your casual speech default?
I use "to." Why? Because one of my teachers back in middle school used "and," and I never really liked her.
Did you intend for that typo to be there? Or does "keep that in mine" have an implied noun? My box, yes put that one in mine. While I believe 'to' is correct, 'and' sounds fine to my ear.
I'm from England, and people say it both ways here. But "and" can't always be used for the infinitive: for example, you can't replace the "to" with "and" in "I'm going to do something". I think it's only after "try" that it appears. I wonder if it originally came from an attempt to be positive, i.e. don't just try to do something, try and do the thing.
I don't think it's necessarily a regional thing. I hear 'and' all the time in California and here in Arizona. It's something that I thing budded out of the expression "Try it and find out." This is pure speculation, but I reason that expression was truncated to "Try and find out" and "Try and see." In either case it still connotes 2 actions. Then, along this same thread, it was used in sentences like "Try and see if it works," from which other sentences with more diluted meaning sprung. In the sentences you gave, I would use 'to' whenever I am fully conscious of my speech. However, there are times when I'm saying things so quickly that I shift into less proper English, at which point "and" might slip in--though it would sound more like "Try 'n keep that in mind."
Its use is almost widespread enough to become idiomatic. To be honest, I haven't really thought about it enough to know if I use it, which probably means I do, at least occasionally.
