次第, the latter event that is to happen has to be done with volition. It cannot be a natural event. It has the nuance of 'having waited for the former event to end'. Your first example cannot be used with '次第' because fire is a natural event. The second one can be, because leaving the factory is a volitional event.
* ドーンという音がして、１分たち次第、火が出てきました。 [Ungrammatical]
A か A ないかのうちに literary means 'within the time span where it is not even clear whether A had happened or not', or 'at around the moment that A is/was to happen'. It does not necessary mean that A has happened yet. Your examples 3 and 4 thus cannot be turned into this construction without the meaning being changed.
'We will let you know about it at around the moment we receive detailed information.'
[It is strange. You cannot tell anything before knowing about it.]
By the way, as I gave in the examples above,
A か A ないかのうちに is usually shortened to
否 (ina) means negation. This construction is comparable to the English
whether or not construction. In English, suppose you have the following example:
whether A or not A
You can avoid repeating the redundant
A by putting the negation, the disjunct
whether altogether, and omitting one of the A s:
= whether or not A
Similarly, in Japanese, instead of repeating A as in:
A か A ないか
you can put the disjunct
か, negation and
か 'whether' altogether. The only difference being that you have to use the negation
否 (ina) instead of the negation
A かないか ==> A か 否 か
If you acknowledge the difference of word order between Japanese and English, you can see that this precisely corresponds to the English phrase word-by-word:
A か 否 か
A or not whether