I was at rowing machine and she was at another machine left front of me. I catch her look at me and one set after she throw a smile at me, I returned. I know that don’t must mean that she want sleep with me but is it I can assume it like a invitation to approach. And what I should say like a opener? Please not some stupid small talk.
How right expression is for “I want to learn you”? Because when I say “I want to learn you” victims of my approach say a couple time “What”, never do not understand me at first.
Third question is a had past year one girl at gym throw a smile and say “hay” to me first and I answered. But hence she do not appear to interested. Only show work out close to me when is a lot people around so I cannot approach her. She is extremely good looking in my book, no 10/10 then rather “it do not go any better then that”. Can I hold that one “hay” from past year like right to approach or “hay” invitation expired.
I’m very in shape guy. Not jecked but very fit.

I'd be weary about approaching girls you see every day, or on a regular basis. My rule of thumb is that if I am a regular someplace that I go to with a specific purpose like work, or at a gym, I don't go out of my way. Instead, I let them initiate. In fact, I intentionally ignore or pretend not to see girls checking me out at the gym. You'll find they will start to position themselves at machines around you so you'll notice them (proximity). Some girls go as far as to say hi or make some kind of small talk.

Long story short when I put my life first, the girls bend over backwards to be noticed...especially when other guys are swarming around them.

Oh, and when a conversations begins, try replacing "I want to learn (about?) you" with "I'm curious about you"

Hope this helps.

You've made eye contact and the girl(s) are smiling? Go for it. I can see that English isn't your first language so I can understand how difficult it must get trying to speak to people, especially women. A great opener in your case would be something like:

Hello, my English is not very good and I was wondering: what does [random word] mean?

She answers and you proceed to mid-game.

Good luck, bud.