In all your sentences, the infinitive is the subject of a verb, sometimes suggested:

[(D’)affronter un adversaire très fort] me met en transe. Rien ne me met plus en transe que [cela]

[(De) vous revoir] me ferait plaisir. Rien ne me ferait plus plaisir que [cela].

Je pensais que [(de) savoir ce qui s’était réellement passé] m’apaiserait.

Each time, I’ve put the verb in bold and the infinitive phrase in brackets.

When an infinitive is the subject of a verb, de-marking is always possible, but only obligatory when the infinitive is post-verbal and a dummy pronoun (ça or il) appears on the verb. It almost always is included with the "Rien ne [verb] plus que + [infinitive]" construction of your first two examples (1). In all other contexts, de appears very rarely, mostly in high-register writing.

In this, this de functions like other prepositions which take nouns as their objects:

(À) Cécile, je (ne) lui ai jamais parlé

Je (ne) lui ai jamais parlé, à Cécile

(De) Cécile, j(e n)’en ai jamais parlé

J(e n)’en ai jamais parlé, de Cécile

So:

When you say "Affronter un adversaire très fort me mets en transe.", you will never place "de" before "affronter", correct?

Incorrect, but this is optional and uncommon.

Then, why is it necessary to include "de" in these three instances? And what is the meaning of "de" here?

It is not necessary. De functions as an optional subject marker for infinitives, although this is not how native speakers are taught to think about it.

(1) But not always, for example this quote from a random blog, writen in a formal register: "Rien ne me plait plus qu’être dans de beaux endroits"

In every of your examples "de" is not an obligation :

Rien ne me mets plus en transe qu’affronter un adversaire très fort.

Rien ne me ferait plus plaisir que vous revoir.

Je pensais que savoir ce qui s’était réellement passé m’apaiserait.

Are correct.

D’affronter un adversaire très fort me met en transe.

Is also correct.

Ça me met en transe d’affronter un adversaire très fort.

Here "d’" is mandatory while it could possibly be replaced with a comma in this particular example :

Ça me met en transe, affronter un adversaire très fort.