Suppose I need new circuit breakers and buy some at a local shop. How do I test them to be sure they haven't been damaged on their way from factory and will do their job when time comes?
Electrical – How to Test Circuit Breakers
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Breakers are supposed to be good for a fairly large number of triggers, and they are supposed to fail open when they fail. Is there a chance that you were running at a heavier overall load when the second incident occurred? I'm thinking that if you were say within 10 amps of max on the main breaker just due to normal load (air conditioners, perhaps?), and caused a short on the secondary (a 15 amp circuit, perhaps), you might have triggered the main to trip first by simply overloading it, before the secondary could draw enough to trip.
If you really think the secondary might be bad, then by all means replace it, but no, you don't have to replace the main just because it tripped. As long as it feels normal when you move it back into position (flip some other breakers to see how they feel - there shouldn't be any slop in the movement), you'll be fine.
The last several times I've seen breakers fail they've all failed open.
Yes you can get pop in breaker replacements.
They look something like this: 
The important thing is to ensure that you use a breaker that is the same ampage as your fuse (or very close to). When I did mine (before rewiring the house) I had some fuse wire that was something like 15A. But the closest breaker was 16A. That's usually ok because the wiring is actually rated higher than that. But for safety make it as close as you can.
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Best Answer
There's no good way to do this. You could (in theory) get a spare electrical box, wire it into your main box such that it had access to more current than the breaker under test, and then install the breaker into that spare box, cause a short and watch it trip.
Alternately, you could install the breaker, overload the circuit in question (borrow all the neighbor's vacuum cleaners?) and watch it trip (and hope nothing goes wrong, causing a fire and burning down your house).
The first is annoying, the second is dangerous (because you have no idea if some previous owner used sub-standard wiring somewhere in your house). There is no good option for the homeowner to test these things.
While I don't think we can make too many general statements, we CAN say that the products distributed in the US are subject to various electrical codes and that the manufacturers design so that if they fail, they fail open. Realistically, you've probably got a lot more to worry about from your appliances, than your breakers.
Just buy your breakers from a reputable retailer, check for damage before installation, and you'll almost certainly be fine.