I've heard before 'eindelijk ben ik beroemd', so I thought it should be OK as well...?!
That's fine a well, it has a bit different emphasis, exactly like the difference I am finally famous! and Finally I am famous!.
Why is there no e on the end of eindelijk?
Is this adjective an exception to the rules?
Because eindelijk isn't an adjective here; it's an adverb and Dutch adverbs never inflect (be suffixed with an e).
Is there an error with "ik ben UITeindelijk beroemd" (marked incorrect)?
Can anyone explain the subtlety between eindelijk and uiteindelijk?
Uiteindelijk is more in the end.
Can you please give examples of the difference? Bedankt!
Why not bekend instead of beroemd?
bekend is 'known' (from kennis, knowledge), beroemd is 'famous' (from roem, fame)