The て-form is the general connective form of verbs and adjectives.
Each of your examples above is a different construction,
合って is not complete (strictly) on its own, but is understood to be leaving the second part off, which could be ください (so it is often used as a short request form).
ている is the present progressive
てから is a construction that means after (verb phrase).
your last sentence isn’t related to the て form, it’s just a use of から。
(i’m not sure if it is natural the way you wrote it, but it would mean “beacuse”)
The て form doesn’t “have” a meaning by itself (not it the sense of one being a noun and one being a verb).
It is a syntactic connective form that has many uses in alot of different grammar constructions.
会って - meet
会っている - meeting
~ている - present tense form
~てから - after
友達に会ってから would mean “After I meet my friend”
友達に会っているから would mean “I’m meeting my friend so…” or “Because I’m meeting my friend”
て form is also used to list verbs. Hope that helps!
友達に会ってから、公園へ行きます。
would mean, “After meeting my friend, I’ll go to the park.”
(〜てから establishes the order of events: first one, then the other.)
友達に会っているから、 公園へ 行きます。
would mean, “I’m meeting my friend, so I’ll go to the park.”
(から after 〜ている implies that the preceding incomplete statement explains the subsequent statement. 会っている is an action that hasn’t been completed, like 食べている, 結婚している, or 楽しんでいる.)