Is it correct to think that these mean the following and when would the sentences below the descriptions of each one of the verbs that I have be preferred to say? Why would one use a reflexive form of the verb? :
ВСТРЕ́ТИЛ - more general notion that includes meeting people for the first time, meeting up your friends, and just seeing someone without even talking at all.
ПОЗНАКО́МИМСЯ - to meet someone for the first time and talk a bit at least, to find out the person’s name and some other things you might be interested in
Я ВСТРЕ́ТИЛ твоего́ брата в метро́.
Мы ВСТРЕ́ТИЛИСЬ с твои́м братом в метро́.
Мы ВСТРЕ́ТИЛИ твоего́ бо́сса в го́роде.
Мы ВСТРЕ́ТИЛИСЬ с твои́м бо́ссом в торго́вом це́нтре.