I don't find either got happy or became happy to be particularly natural. I would simply use was happy, and leave whether that is an observation or a contrast with a previous state to be understood from context:
She had been irritable all through dinner, but now that the stag's obnoxious friends had departed, the hen was happy.
Leaving that aside, it is true that some meanings of the extremely versatile get mean become, specifically:
- Reach or cause to reach a specified state or condition
[ODO] Worth noting is the usage note:
The verb get is in the top five of the most common verbs in the English language. Nevertheless, there is still a feeling that almost any use containing get is somewhat informal. No general informal label has been applied to this dictionary entry, but in formal writing it is worth bearing this reservation in mind.
In other words, get happy would be more common in conversation and in informal writing, whereas become happy would be more acceptable in formal registers. That is broad a generalization, but it has usage implications.
Get has a somewhat greater connotation of agency or intent, perhaps because many of its other meanings are causative, and refer to inducement, deliberate movement, or inflicting injury or punishment. If I say I got drunk on cough syrup, I may be interpreted as intentionally drinking cough syrup to get drunk. If I say I became drunk on cough syrup, I am distancing myself from the act, saying the drunkenness was unintentional.
Become being more distant and thus "softer," it is much rarer as an imperative, in verbal communication or informal writing. Get is more direct, whether you want to be forceful— Get ready! Get cracking! Get out!— or more personal— Get well soon!
For additional usage notes, BBC Learning English has a unit on 'Get' and 'become'. At EL&U see Is “get” (in the sense of “become/make”) appropriate for formal writing? and He was getting vs being beaten among others.
Note also that get is involved in a large number of idioms, some vulgar. If John and Mary are lollygagging around the office, their manager must be careful about saying The two of you should get busy as that can be taken to mean that they should have sexual relations. Similarly, get happy to Americans is more likely to be taken to mean getting drunk or high on marijuana than as a reference to a Judy Garland song (which was probably performed by a Judy Garland who was both).
Both are acceptable (yes, I know I'm the one who said you were wrong), but used will induce fewer corrections :)
Various opinions:
English Grammar Today has this to say on this exact topic:
The negative of used to is most commonly didn’t use(d) to. Sometimes
we write it with a final -d, sometimes not. Both forms are common, but
many people consider the form with the final -d to be incorrect, and
you should not use it in exams:
It didn’t use to be so crowded in the shops as it is nowadays.
I didn’t used to like broccoli when I was younger, but I love it now. (Don’t use this form in exams.)
In very formal styles, we can use the negative form used not to:
She used not to live as poorly as she does now.
Language Log suggests that used is preferred by English users at large (but of course as good descriptivists they offer no comment on which should be preferred...)
Over at EL&U use is agreed to be 'more correct', but is firmly in second place behind 'rewrite to avoid'.
BBC World Service Learning English is firmly use.
Best Answer
There are different differences within the examples as presented (which I'm sure aren't exhaustive regarding possible distinctions, but let's stay focused).
I've included a third alternative because that's a more common version that most closely matches 1a in implication (working together is what we're used to / expect). 1b could imply we might not even have wanted to work together when we started (but now we've come to tolerate, bear, put up with the situation.
Where 2c replaces non-idiomatic 2b. I can't really see any scope for saying either version could imply anything different to the other. I'm sure 2a would be far more common in relaxed speech, but there's wrong with the slightly more formal 2c.
Where 3a implies that he didn't want to keep finding fault(s), but they were there and he couldn't avoid them (perhaps he worked as a Quality Inspector). After a some time, it no longer bothered him that he had to keep finding fault(s).
3b, on the other hand strongly implies that he does want to find fault. Similar to 1a above, in that the implication is he both wants and expects to do so.
Unquestionably here, 4a implies that originally you didn't like drinking neat liquor, but you had to do it so often you can now at least tolerate (and even perhaps enjoy) it. Whereas 4b might be a somewhat "imperious" request / command (Give me a glass of neat liquor, because that's what you normally have, and it's what you're expecting now). Or a withering complaint, if you've just been handed a glass of watered-down whisky when you wanted it full strength.
The main difference (apart from the fact that used to is much more common than accustomed to), is that usually, to be / get used to is more closely associated with adapting to a situation (through past exposure), whereas to be accustomed to often implies expecting / wanting some past pattern to be repeated in a current or future situation.