Uyan Ey Gözlerim

I need to see the original (in Arabic/Ottoman alphabet) to make sense.

Well, you could read and / or download the diwan from here:
http://ekitap.yek.gov.tr/store/AdvancedSearch.aspx?value=&Name=True&code...Üçüncü%20Murad
(Yazma Eserler Kurumu's official site)
from where I downloaded :) This is in syllable meter not in Aruz meter (if not different aruz patterns are used for different lines which is unlikely) so it is unlikely be a part of a diwan.
Apparently this is the original source of the image you mentioned (I did an image-search):
https://www.chandos.net/chanimages/Booklets/GS4501.pdf
pp 26-27
It reads:
Uyan ey Gözlerim (Tr. 5)
Collected by Ali Ufki
MS Turc 292, page 298r
National Library of France, Paris

It seems pretty credible
I wanted to look at the original script because I thought it could've been dil u dillerince but apparently it is not.
There is no way the second letter is ye, there is no dent, it is clearly an L (two Ls). And the last letter reads a y (i) not a w (u) so it doesn't read dillu. It seems like there is a shadda on L (but probably it is just a stain). So it could have been delelli (delel as a short form of delal) and it would make sense in the context.
(see: https://www.osmanlicasozlukler.com/ingilizce/tafsil-462229-h86.html and https://www.osmanlicasozlukler.com/kamusiturki/tafsil-258105-c69.html). (I also considered delilli or delîlî but a y is missing).
But the syllable count changes so I think we have to read it as dilli (as everybody did) and in that case I guess the sentence means something like: (every creature) who has a tongue starts to praise God in their own language.
Note: There are some other differences in that document; a stanza is missing, it is not alemlere but mü'minlere etc. So I guess there are different manuscripts with slightly different scripts. Probably it reads dillu in another manuscript which means dilli:
https://www.osmanlicasozlukler.com/ingilizce/tafsil-462236-hg6.html

That suffix makes deverbal adverbs so can't be attached to nouns.

1. Clearly he is not saying dillu but I am not sure what he says. Probably he says dil-i dillerince as many Turks (especially young ones) who don't have any education on old literature, Persian or Arabic over-use this Persian structure whenever they hear an old text. It was indeed very commonly used in Ottoman literature but they over generalize it as if Ottomans never used several Turkish and Arabic i suffixes. Still I think dilli is acceptable even though I don't hear a second L.
2. No, I hear suyun. Try to listen in x0.75 speed, I think you will hear too.
3. No, I hear the first one suçumu and the second one suçum.
Benim, Murad kulun, suçumu affet
Suçum bağışlayıp ...

BTW, as you noticed I think, suyun instead of suyunu is a nice example for the archaic usage (dropping accusative suffix after possessive) we recently discussed for another song.