Is it permissible to say that one of the Rightly Guided Caliphs or the Companions erred in word or deed, considering that they are not infallible, and what is the ruling on the examples mentioned for that?

None of the Companions are infallible, and they may err. Therefore, reporting their errors is permissible, provided their virtues and Allah's forgiveness for them are also mentioned. However, it is forbidden to report their errors with the intention of disparaging them. 'Umar's supplication through the prayer of Al-'Abbas was not an error; rather, it was seeking the blessing of a righteous man. What happened between 'Uthman and Abu Dharr was a political ijtihad (independent reasoning) for the benefit of the Muslims. The fighting that occurred among the Companions was due to ijtihad; the one who was correct receives two rewards, and the one who erred receives one reward. It is obligatory to refrain from discussing their disputes, and to love and praise them. Their errors are forgiven due to their ijtihad, or they are but a drop overwhelmed by the oceans of their virtues.