What would happen if the water disappeared?

Subjunctive II - “would” or “would”?

Every German verb has two ways of forming the Konjunktiv II. The first one is what linguists call synthetic, i.e. via inflection. For strong verbs, These forms look like past forms, but with an added ending -e and umlaut if possible:

past indicative - past subjunctive / Konjunktiv II
had - would have
was - would be
came - would come
went - went

Note that some verbs have different vowels in the past indicative and past subjunctive: stand, stand, stand.

For weak verbs, past indicative and past subjunctive are identical.

When I lived in Italy back then ... (= was, past indicative)
If I lived in Italy now ... (= would live, past subjunctive / subjunctive II)

Note that although the form is called past subjunctive, it refers to the present and the present only! This will be relevant below.

Probably because this ambiguity between past indicative and past subjunctive is hard to tolerate, a second way to form the Konjunktiv II has developed. This is what linguists call analytic, i.e. by combining two words, namely a form of would plus the bare infinitive.

would have, be, come, go, live, ...

So far so good. Let's apply this to your examples.

If he did today would come!
If he did today would have come!

The first example is simply the analytic subjunctive II of come. It is desirable for him to come, but it is not yet known whether he will do so or not.

The second example is the synthetic subjunctive II of to have come. Above I mentioned that the Konjunktiv II by itself always refers to the present. However, in this case a perfect auxiliary (be) appears in the Konjunktiv II, which means the second example refers to the past: It would have been desirable for him to come, but he did not.

The other set of examples shows the same kind of difference.

I would gladly to celebrate.
I would gladly to celebrate.

The first example is the analytic subjunctive II of to celebrate. I have the desire to party, but am not partying at the moment.

The second example is the synthetic subjunctive II of to be (celebrate). However, be plus infinitive is a tricky construction. It could be interpreted as

I would like to celebrate went.

with would have gone as the synthetic subjunctive II of to be (gone), with the expected meaning: I would have liked to go partying, but did not in fact do so.

If ellipsis is ruled out, it could be an instance of the construction discussed in this question. The basic meaning is telling someone where you are or will be, or, in the Konjunktiv II, where you would like to be but are not.

I would yes for a long time to celebrateif my friends had picked me up on time!
= I would long time at the party, if …

To be frank, the first time I read

I would like to celebrate.

I thought you had mixed the synthetic subjunctive II of be (would) and the analytic subjunctive II of to celebrate (would celebrate). Could this be the case?

I would at the party too, if I could.
I would also celebrate with, if I could.