Help with installing 2 breakers
I couldn't identify any breaker with only two white wires, but the 10 breakers at the bottom each have two white wires plus one black. This is because they're arc fault (AFCI), ground fault (GFCI), or combination of the two functions. Those kinds of breakers have to monitor the current through both the neutral and the hot lines. The white jumper from the neutral bar to the breaker makes this possible.
The breakers that have only one black wire connected to them are conventional breakers. The neutral wires corresponding to these are attached directly to the neutral bus bar.
The connection of the new all-in-one breakers is just as you said. The white pigtail should connect to the neutral/ground bus bar, and the ground conductor from your new circuits goes there too. If the pigtails aren't long enough you can extend them with a piece of same-gauge white-colored wire joined with a twist-on connector (aka wire nut). Then the black and white wires from the new circuits go to the line and neutral terminals on the breakers. Position matters; the breaker will be marked in some way to indicate which terminal is which.