bike wrench

what link?

You didn't share a link. I'm assuming you mean a center stand. It's probably fine, but you'll want to check with the manufacturer.

I would put at least three kickstands

You're only going to danage the frame if you have a child larger than the rating for the child seat/rack. You'll pull the steel bolt through the mounting plate before you damage the frame.

You will be an outlier oddball for putting a kickstand on a dropbar bike, but the kid's seat is odd too.

You do you, but after a quick image search, that is a bit compact of geometry to load with weight, especially extended off the back IMO

The wheelbase distance (between centers of each wheel), dictates how a bike will handle and what kinds of loads can be carried. Road race bikes have very short wheel bases. The quick way to spot the overall geometry is how close the rear wheel is to the seat tube. Here is the most extreme possible road and the classic goto long haul touring bikes:

Most people don't put a kickstand on a drop bar bike because it is just dead weight. You can easily lean the bike against stuff. The other pro trick is to use the weight of the bike and the forward pedal on top of the curb side of with the wheels on the road. The ratchet paws will only let the wheel and pedals spin one direction. You use this resistance to let the bike hold itself up against the curb.