word choice - Flat tyre and puncture

Please read the following sentences:

1. My bike has had two punctures in the last three weeks.


2. I got a flat tyre.


3. My bike got a flat tyre.


4. My bike got punctured or The tyre of my bike got punctured (Which one is correct?)

In the first sentence, from Cambridge, 'puncture' is used as a noun. But can it be used as a verb, like in the third and the fourth sentences?

Could you help me understand when to use flat tyre and when to use puncture ??

Consider the situation -

If I am late to the office and I want to give this excuse of puncture, then how should I frame my sentence? And will that sentence be applicable to bicycles, bikes, cars, buses (public transport) or any other transport.

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Is the word 'puncture' used in American English ??