As has already been explained, iūcunda is neuter nominative plural modifying quae, which has omnia as its antecedent. And the translation of omnia, quae iūcunda...accidere possunt into English would be 'All pleasant things that are able to happen.'
Now, you might ask yourself why iūcunda is being translated closely with the omnia in the sentence's main clause, even though it doesn't appear in that clause, instead of being translated with quae in the relative clause, where it does appear.
Gildersleeve & Lodge, Latin grammar §616.3 explains this:
Adjectives, especially superlatives, are sometimes transferred from the substantive in the principle clause and made to agree with the Relative in the Relative clause.
One of the examples that G&L provides is:
Nēminī crēdō, quī largē blandust dīves pauperī, Pl[autus], Aul[ularia], 196; I trust no rich man who is lavishly kind to a poor man.
In other words, the sentence from Plautus is equivalent to Nēminī dīvitī crēdō, quī largē blandust pauperī, but dīvitī has been moved into the relative clause and made to agree with quī. Likewise, your sentence from Cicero is equivalent to Nam mihi omnia iūcunda, quae ex hūmānitāte alterius et mōribus hominī accidere possunt, ex illō accidēbant.