Should we use reported speech only after 'said'?

Should we use Reported speech only after ‘said’ (I said…You said etc.)??? What about other verbs? For example : I found out…I noticed…I knew…
Are these sentences correct?:

  1. Kate is pregnant.
    I found out that Kate is pregnant (is- because the situation hasn’t changed) or should I say:
    I found out that Kate was pregnant.?
  2. You fastened your seat belts.
    I noticed that you fastened (or had fastened) your seat belts.?
  3. You wrote to my mother .
    I knew that you wrote (or had written) to my mother.
    Does sequence of tenses mean the same as reported speech?

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These are all examples of tense sequence or tense regression:

I found out that Kate is pregnant.-- Yes, still pregnant
I found out that Kate was pregnant.-- regression of the verb
I noticed that you had fastened your seat belts.
I found out (because ‘know’ still holds true) that you had written to my mother.

Does sequence of tenses mean the same as reported speech?– Reported speech is one kind of tense regression; it is as it says, ‘reporting’, so usually takes such verbs as say, ask, demand, etc as the main verb.
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Thank you Mr Mister Micawber.
Please tell me when should I change the verb(s) in subordinate clause to its/(their) past forms and when not? When the situation hasn’t changed I shouldn’t change the verb to its past form?

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You can always regress the verb; you can also choose not to regress it if the condition or situation still obtains at the present.

Mr Mister Micawber thank you very much. Your explanation is clear.

Mr Micawber, so:
1.We use tense sequence or tense regression when/if there is past verb in the main clause,right?
2. We don’t have to change Past Simple in Reported speech to Past Perfect, but we can. Do we have to change Past Simple to Past Perfect in tense sequence/tense regression or it also can be:
You fastened your seat belts.
I noticed that you fastened your seat belts.?

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1-- Right.
2-- I think you should, usually.
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Thanks Mr Micawber.