You’ve asked many questions some have no answers that I know of.
Firstly, he was brought (not sent) to Rivendell by his mother Gilraen shortly after the time of his father’s death. He was given the name Estel to hide his lineage as the last living descendant of both Isildur and Anárion.
His mentor was likely Elrond, although I expect he would have had many tutors. With his mother living in Rivendell I would suggest Westron as his cradle tongue, but Sindarin as the language spoken most with other residents of Rivendell.
I expect he learned Sindarin and Westron, and probably both Tengwar and Cirth scripts. Other children of similar age would be unexpected.
His lineage and responsibilities were not revealed to him until he was 20, and when they were it would most likely have been Elrond [an Elf-lord, his nearest living relative (other than his mother), and a lore master] who taught him.
I would expect that he learnt his woodcraft from many Elves of Rivendell, and refined it further when he returned to his people.
His time as Thorongil was to intimately learn of the south kingdom and address issues that he saw that couldn’t wait. The description of this time of his life suggests to me that it was self-assigned, but I’ve not found anything definitive.
We know that the Shire is a somewhat literate culture, especially amongst the Tooks and relations. This literacy would be in Westron and dialectal additions and seems to have been taught within the home.
Sam learnt more from Bilbo than Frodo. Frodo would have learnt Elvish from Bilbo, who would have learnt it from various Elves, including Elrond.