1)
足が/の速い means "to be fleet of foot", as the same structure as 背が高い "to be tall" or 頭がいい "to be clever".
あんまり means "excessively". This is not negative.
2)
Yes, the second と is conditional.
聞く is active, not passive 聞かれる, thus, the subject is 友だち, not 走る名人.
The narrator is not 走る名人, so it's "his friend", not "my friend".
3)
隠れる[かくれる] is intransitive, and the transitive pair is 隠す[かくす]. He hides nothing.
みんな means "all (of the tasty food)". This is the object, not the subject.
4)
"お + the -masu stem of a verb" is a soft/tender imperative form, often said by adults to children.
e.g.
お食べ (tender version of 食べろ/食べなさい)
お行き (tender version of 行け/行きなさい)