I doubt you'll be able to breed your cat's personality into any kittens, especially from the father's side, because the father is usually hands-off. (Hopefully someone with more experience in that area can chime in here.)
If you have human children (or brothers and sisters!), you'll know that even with people, you can't predict personality from the parents, or even from each other. Most of us know human sib groups in which all 3 sibs are as different as can be.
Since the female comes up onto your balcony with ease and she is used to eating food you give her, first of all I would recommend contacting a local cat rescue group and asking to borrow one of their traps.
Someone on these boards based in the US can help you find such a group if you have trouble. Feel free to ask if you need help.
Alternately you can buy a trap.
Here is a page that has information at the bottom about where to buy traps:
...plus other useful information at the top.
Females are notorious for not wanting to go in traps, especially if they are smallish/too narrow. So try to get a bigger one if you can.
The traps are surprisingly simple to use. In the case of females, some people suggest setting the trap in such a way that it can't spring shut for the first few nights, to get her used to the idea, just because they are so incredibly cautious.
How recently was she pregnant? If she is still nursing her kittens, the rescue group might ask you to wait to try to trap her. If she is still pregnant, they'll want you to trap her right away, obviously!
As for having more cats with your cat's beautiful looks and personality, you might want to pop in to one or two of the shelters to see what's there. One of the benefits of adopting a cat rather than having a litter (besides not adding to the cat population) is that you know what you are getting, as the cat already has a certain personality and appearance, whereas birthing a litter gives you no guarantees at all, in looks or in personality, especially from the father cat, who usually is hands-off in raising the litter.