Get vs become

I think
to get I would use in the now/present
I get hungry at around 9am.
I get hungry at around lunchtime.

To become I would used in the past with another clause
I became hungry as I did not notice the time
I became hungry as I walked a long distance

I become hungry in the present does not sound right to me.

There was...

once a firm stand (in the UK/Commonwealth) against using get in serious writing because it was a lazy way of saying things and regarded as more for informal dialogue than serious writing.

In your sentences, boron, become would have been used.

You might also say "grow hungry" or "grow excited."

A simple "was/is" works for pregnant.

As for "drunk," since it isn't particularly formal in the first place, "get" sounds better. "Become" works better with "intoxicated" or "inebriated."

I think the context would have significant impact...

Consider a sample of colloquial dialogue:

"Oh man, I just wanna get laid!" (become wouldn't work here)

"No glove - no love! I'm not gonna become pregnant!" (get would work)

Craft it in the fashion that best fits your story.

boron said:

So, there's no reasoning behind this other than "get" being informal and kinda reserved for a spoken English?

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Yeah, bar conversation, it's pretty rare. I suppose the reasoning is 'get' is very versatile and a good verb to use when you have little time to plan your words.

I got a card in the post today
Go get my boots
I got laid.
I have got to get that...

When it comes to writing (any register really) lexical variety is what gives your writing spice, so other verbs / forms of passive / modal usage regard 'get' is more natural when you have time to pre-plan: got would be substituted.

But it's not saying that you can't use it in writing (dialogue would be a good place to reflect its use etc).

boron said:

So, there's no reasoning behind this other than "get" being informal and kinda reserved for a spoken English? (I do understand the meaning of "get" and "become" as independent verbs, though).

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I think you're right to use "kinda." I suppose you'd be pretty safe if you go with what you're saying--"get" for less formal and "become" for more formal. But I'm not sure if that rule will work every time.

You could use "grow" for some things. He grew hungry. [or] His hunger grew.