Of course dawned on me has a tense - it's just that in practice it's usually past, for the same reason we tend to speak of realising things in the past (you can't know something until you know it). But it can be...
present:
It dawns on me that...
(or more rarely)
it is dawning on me that...
future:
It will dawn on you that...
conditional
It would dawn on me that...
etc., etc.
It seems to me OP's confusion stems from the fact that s/he expects some grammatical connection between when you realise something and the timeframe(s) of the thing(s) involved in the realisation. There is no such connection, obviously. It might dawn on you tomorrow that the universe began 15B years ago, or it might have dawned on you yesterday that it will end 15B years from now.
In the case of OP's final example...
It dawned on me that the fact that he lives there didn't bother me at all."
...there's some semantic justification for saying dawned and didn't would normally be the same tense, simply because the realisation and the lack of concern would often be concurrent. But it might be what's dawned on you is you will not be bothered at some time in the future (even though you might have been bothered when you realised this, and you might still be bothered when making the observation later).
Other possible temporal relationships between the three highlighted verbs are also perfectly credible. What dawns on you may be that you are not bothered now (or will not be bothered in the future, or would not be bothered in a hypothetical scenario) about the fact that he will/might live there.
Your initial instincts were better. It's about time she came home.
It is a subjunctive. But better would be
Yes, she should be home by now.
When your wife or daughter finally arrives, very late, then you would say:
It's about time she came home!
EDIT: You would exclaim the above only after wife|daughter had finally gotten home because it means The person has done what was expected of him or her (in this case, gotten home) but has taken a very long time to do it. Another example: diner at a restaurant waiting a very long time for the waiter to come over to his table. Waiter finally arrives. Diner says curtly:
It's about time you came over! or It's about time you waited on me!
The Sun-Times example We did the documentary about four years ago. It's about time to go back and do a follow-up. has an infinitive "to go" after "it's about time" whereas your sentence has a past-tense "came" (acting in a subjunctive role). The Sun-Times scenario is not an analogue for your situation.
The follow-up is due. Your wife|daughter is overdue.
If the documentary producer wanted to convey the idea that the follow up ought really to have been done long before now, that too much time has elapsed, he would say:
It's about time we went back and did a follow-up.
EDIT 2:
And to confuse things even further, intonation pattern can change the meaning.
It's about time she came home!
means she has not yet arrived and is long overdue.
It's about time she came home!
means she has finally arrived home.
Best Answer
When you start a sentence with a clause based on as time goes by, the second clause describes what happens as the time is passing, and so it has to be of the same tense as the as time goes by clause. You can't, for example, use present simple in the first clause and present perfect in the second clause.
We use the simple present to talk about general truths: things that were true in the past, are true now and always will be true.
We use present perfect to talk about things that have taken place over a period of time and are still happening, or things that happened in the past and have some lasting effect (for example making a reservation).
Realising that the earth is not the centre of the universe is something that happened a long time ago: it is no longer an issue. It therefore makes more sense to use past simple. For past simple, we want a verb that expresses an event rather than a state, so learn works better than think:
Two other comments about your sentences. First, people is plural, so it's people think, not people thinks. Second, if we want to talk about the planet we live on, we ususally (but not always) use the definite article the earth. The capital letter on Earth is optional.