I've collected and grown plants from both.

Yes; the imaptiens should have light brown/brown seeds. The white ones aren't ripe yet. If they have snapped off the branches, they weren't. If they were ripe, they would've already popped open when they hit the ground. The ones I've picked have always been still on the branches, and are bright green and fat. I usually collect them by snipping off the branch the pod is on, and then gently put them into a cup, which a lot of times enough to pop them open. They aren't called 'touch me nots' for nothing!

As for the begonias, definitely let them get nice and brown until they are practically falling off the branches before gathering. Then, dry them well and store them until you are ready to sow, sometime in early winter. Mind you, I've only gotten a few plants from many pods. They are indeed dust size, and very tempermental. I rubbed the pods gently over the soil and hope for the best, but germination is slow and really tiny. But if you do get some to germinate, be patient and you will be rewarded with beautiful plants that are tougher than the store bought ones. I put mine out in the winter sun on a windowsill and they never burned in the summer sun.

The ripe impatiens pods turn light green, get bulbous, and lean at a right angle to the stem. The ripe pods will come off stem with very little effort. These pods usually have mature seeds. I grab them from below with three fingers and gently remove them from the stem ("sneak up" on them). I then squeeze and burst the pod over a cool whip container to save the seed. I dry seed and burst pods in a pie tin until dry enough to sort out seed.
Previous poster covered begonias quite well - I have nothing to add.
Have Fun!
TK