Baby bunnies can’t bond. Even if they are littermates, they are not bonded. Bunnies need to be spayed/neutered before they can be bonded. So you’d have to keep them separate for months. This is due to the fact that hormones give them the desire to only breed and mate. Baby bunnies are often incorrectly sexed, so even if you think you’re walking away with 2 boys or 2 girls you may very well actually have one of each or even have both be the complete opposite gender. If you’re worried about the procedures, why don’t you adopt an already bonded pair from a shelter, if you want a pair? Age has no affect on how well they bond with you or with each other. If you buy from the breeder you will be waiting anywhere between 5-8 months to bond them depending on their genders.
As a general rule, bunnies don’t like being picked up. That’s not because you didn’t bond with her. The majority of bunnies do not like being picked up. They are prey animals by nature. Would you enjoy being picked up by someone 6 times your height? The best way to bond is at their level and sit on the floor with them. Every bunny is different personality wise. Breed doesn’t have any affect on personality, neither does the amount they are handled. What age you get them at has no bearing on how they bond with you. Some bunnies take months to open up even a year or two and other bunnies are very loving immediately. Again, it’s not an age thing.
To answer your other questions: just because one rabbit had the heart condition doesn’t mean the rest do. It really is just genetics. It would all depend on who the parents. Considering neither are obviously fixed, you wouldn’t know if they had it. As for males, like I said it’s really tough to accurately sex at 8 weeks and under, but if they are males, the procedure is much less invasive, but complications can still happen. Males aren’t more or less likely to bond than females. It all boils down to the personalities of the bunnies involved. Two males can be perfectly happy together just as well as two females. Though, two females would be a bit tricky because they can be notoriously territorial and aggressive.
Hope this helps, and I’m so sorry for the loss of your precious Ginger. Binky Free Ginger