Immediate actions are defined as follows:
Immediate Action: Much like a swift action, an immediate action consumes a very small amount of time, but represents a larger
expenditure of effort and energy than a free action. However, unlike a
swift action, an immediate action can be performed at any time—even if
it’s not your turn. Using an
immediate action on your turn is the same as using a swift action, and
counts as your swift action for that turn. You cannot use another
immediate action or a swift action until after your next turn if you
have used an immediate action when it is not currently your turn. You
also cannot use an immediate action if you are currently flat-footed.
Immediate Actions start in the order they are announced. In your example Wizard A starts casting Apocalypse from the Sky, Wizard B cast Celerity and then combust, then Wizard A casts Celerity and counterspell.
This would then resolve as the counterspell countering the combust, and then the Apocalypse coming.
So in answering your numbered questions:
1) Yes
2) Once Wizard B announces his immediate action it has started and would complete except for the counterspell of Wizard A. Wizard A's counterspell starts a tiny bit later than Wizard B's combust. So no issue there.
3) See 2 above
4) Celerity would cause Wizard A to be dazed (unless he was immune as you have suggested). If not immune I would allow him to complete his Apocalypse spell but I think the RAW answer would be that he could do nothing after the action he gained from the Celerity.
The bless spell is not interrupted
The key to the answer is:
You briefly stop the flow of time for everyone but yourself.
For everyone else, delta t is zero.
No time passes for other creatures
Turns / rounds each last six seconds -- six seconds elapse from the beginning of someone's turn and the beginning of their next turn. From this game mechanic, we can say that the usual delta t from round to round is six seconds. Spells with duration of a minute can be modeled as being on a counter in this case: you count down one for each turn/round elapsed.
For everyone who is not the archmage, their time / turn / round counter remains where it was when time stop went into effect. Since no time is passing for them, the durations of their spells are, compared to the archmage's frame of reference, extended. The archmage's delta t keeps moving. For the other characters, they don't notice a difference since for them time stopped.
The bless spell's duration depends on the caster
In the case of bless, a concentration spell, the duration is keyed to the character who cast it, which is also the character who is concentrating on it. If it is a character who is not the archmage, their delta t is zero so their duration counter resumes on their next turn. (That is after time stop ends). Their spell still lasts a minute for them because time (and the counter) stopped for everyone but the archmage. That would provide the archmage with a few extra rounds / turns of the bless spell's magical effects.
If the archmage cast bless (from a ring of spell storing) it's duration would keep decreasing since time/turns are ticking away for the archmage.
@Medix2 asked for clarification in a comment:
If bless were cast by somebody else, but cast on the Archmage, would they benefit from it?
The answer is: yes. Nothing in the time stop spell says that it stops the effects of other spells. Bless, once it takes effect, keeps on taking effect until the spell ends (or concentration ends). Nothing in its text says otherwise.
Concentration
Some spells require you to maintain concentration in order to keep their magic active. If you lose concentration, such a spell ends. (Basic Rules p. 79)
In plain English, you in those two sentences is the caster of a spell requiring concentration. Unless you lose concentration, the spell does not end.
Best Answer
Reaction generally occur after their trigger and so cannot interrupt the casting of a spell
The Ready action is no exception to this rule so when Bob casts time stop Alice cannot actually interrupt the casting. This means that Bob's time stop will go off and he will receive the 1+1d4 turns while Alice cannot do anything.
Immediately afterwards Alice's Readied action will trigger and she will cast time stop, granting her 1+1d4 turns.
After Alice's turns it will go back to the rest of Bob's turn (the turn on which he cast time stop). This seemingly odd outcome (Bob acts, Alice acts and then we're back to Bob) is in accordance with answers to the following questions:
However, castings can be interrupted using counterspell
Unlike the Ready action, counterspell takes place before a spell's effects; it explicitly allows you to interrupt the casting of a spell.
As such Alice could interrupt Bob's time stop and Bob could interrupt Alice's time stop (also, either one could interrupt the other's counterspell assuming they hadn't already used their reaction in an attempt to interrupt time stop)