I think I am getting very confused with past tense questions!  So can I check that I have got this right or wrong?

Asking questions with adjectives, the ´to be´ suffix is added after ´mi´ with a ´y´ buffer consonant.
e.g  Yorgun muydun? - were you tired?

Asking questions with verbs, the ´to be´ suffix is added to the verb stem exactly as the statement form and the ´mi´ is added afterwards on it´s own.
e.g. Koştun mu? - did you run?

Is that correct???

´´ your examples are absolutely correct..

Yorgun mu idin = as a seperate version but its not used commonly..

Yorgun mu+y+du+n common way to use..(modern turkish)

Koş+tu+n  mu ...= here ´´mu´´ a question item..so for words the question item comes last.

İzle-di+n  mi  = did u watch ?

hapşir+dı+n mı ? = did u sneeze..

Why is the ´y´ needed?   Is it a buffer consonant?   It is not separating two vowels.

Cos the letter ´´y´´ connects two vowels..so now you will ask me where is the two vowels ..the rule is in turkish two vowels can not come next to next..

yaa is not right..yana..it connects two a´s with n..so in this case n is connecting two vowels..so in our case where is two vowels next to next..let me show you..

yorgun + mu + idin (as i explained earlier..its original form was mu+idin.  so there is a problem as two vowels (u and i )must not come next to next..so what happened was ´´i´´ dropped..and ´´y´´ came..so lets read it now.. muydin..still doesnt sound right ..cos after the vowel ´´u´´ should follow with ´´u´´ as the VOWEL HARMONY...so lets look at the finish   MUYDUn.. MU+Y+DUN..

hope it will help you understand..

Evet, şimdi anladım.
Çok sağol.