Answers to all those questions would take a mighty post, but I can start off, at least, by saying that Galadriel was not the only Exiled Noldo in Middle-earth, as, for example, Gildor Inglorion was also an Exile.

I should probably not go into some of the earlier stuff since you have yet to read The Silmarillion. Don't want to spoil everything! Part of an answer then, might go...

Imladris (Rivendell): 'mostly' High Elves (The Road Goes Ever On). 'Elrond retreats with remnant of the Noldor and founds the refuge of Imladris' (Appendix B, The Return of the King). 'After the fall of Gil-galad, Master Elrond abode in Imladris, and he gathered there many Elves...' (...) 'In Eriador Imladris was the chief dwelling of the High Elves; but at the Grey Havens of Lindon there abode also a remnant of the people of Gil-galad the Elvenking.' (Of The Rings Of Power And The Third Age).

Mirkwood and L’rien: mostly East-elves (Tolkien, The Lord of the Rings). These East-elves were probably a mix of Nandor and Avari (at least according to some texts). Some Sindar migrated from Lindon in the Second Age and ended up in Mirkwood. Some Sindar and Noldor ended up in L’rien.

'The People of L’rien were even then [i.e. at the time of the loss of Amroth] much as they were at the end of the Third Age: Silvan Elves in origin, but ruled by princes of Sindarin descent (as was the realm of Thranduil in the northern parts of Mirkwood, though whether Thranduil and Amroth were akin is not now known*). They had however been much mingled with Noldor (of Sindarin speech), who...' JRRT, History of Galadriel And Celeborn, Unfinished Tales

Lindon had a mix of Noldor and Sindar. In the first edition of The Lord of the Rings there are explicitly Noldor in Lindon according to Appendix B, before some went to Eregion. In the revised version Gil-galad dwelt in Lindon north of the Lune (south of the Lune dwelt for a time Celeborn). Later some of the Noldor went to Eregion. In a note published in Unfinished Tales it was said that south of the Lune were largely Sindarin Elves. In the Third Age a 'remnant of the people of Gil-galad' dwelt at the Havens. Some terms:

Noldor 'The Wise, Those who know'
Sindar 'Greys, or Grey-elves'
Nandor 'Those who go back' (often interpreted this way)
Tawarwaith Silvan or Wood-elves
Avari 'Refusers'
High Elves can refer to the Exiled Noldor with respect to Elves of Middle-earth and sometimes seems to have a more general application.

This is only the top of the mountain with respect to the Elvish clans and migration, and the names of clans. Incidentally the nomenclature here does not include ideas newly published in Tolkien's Words, Phrases, and Passages.

Grey Havens (Mithlond) on the Gulf of Lh’n was the dwelling place of C’rdan the mariner and shipwright. C’rdan was one of the wisest and oldest of the Sindarin Elves.