Is speaking about personal problems or problems with colleagues for the purpose of seeking advice or providing an example considered backbiting (gheebah) or slander (nameemah), whether the name is mentioned or not, and similarly, is mentioning historical events to learn lessons from them considered so?

Gheebah (backbiting) is mentioning your brother with what he dislikes. So, if you mention a person with what he dislikes and by his name, then that is considered forbidden gheebah, except in a legitimate consultation, or for advice and warning, while limiting it to what is necessary. If you speak about a problem without mentioning the name of its owner or what identifies him, then that is not gheebah, just as the Prophet, peace and blessings be upon him, used to do by saying: "What is wrong with people who say such and such?" Likewise, it is not gheebah to mention a person with something that does not involve harm. As for mentioning what is confirmed from ancient history about a specific person, there is no harm in it, with the intention of clarifying his state.