Kun uni keskeytyy, olen surullinen aamulla.

kun means when and introduces a clause stating that something does happen (or habitually happens).
jos means if and makes the clause conditional (something might happen).
Using kun here tells us when sleep is interrupted (as a real or recurring event), not merely if it happens.

No. keskeytyy is the 3rd person singular present of the intransitive verb keskeytyä (“to get interrupted”).
• It means “it becomes interrupted” or “it gets cut off.”
• The true Finnish passive of keskeyttää (to interrupt) would be keskeytetään (“it is interrupted [by someone]”).

Yes. You add the genitive plus a possessive suffix:
kun uneni keskeytyy
Here unen is the genitive of uni and -ni marks “my.”

Finnish verb endings show the subject:
• -n on olen already means “I am.”
• minä (I) is optional and used only for emphasis or contrast.

After the verb olla (to be), predicate adjectives stay in the nominative to agree with the subject.
Since the subject is implicitly minä (I), surullinen is nominative singular.

aamulla is the adessive case (stem aamu- + -lla).
In Finnish, the adessive often expresses time at which something happens: “in/at the morning.”

Yes. aamuisin is an adverb of habitual time meaning “in the mornings” (regularly).
Example: Kun uni keskeytyy, olen surullinen aamuisin. (Whenever my sleep is interrupted, I am sad in the mornings.)