sakam is understood, but we use “shtem” in the west and in the east they say “iskam” which is coincidently also the literary form. Actually, they use “shta/shte” in the east too, “shtem” is plural, whereas plural in the west is “shteme”.
Hence, I suspect “shte” is equivalent to the english “will”. And “ke” and the rest are derivative. But don’t quote me on that.
“dast” (or is it dati? lol) is I believe the infinitive, hence why it sounds foreign to you. Bulgarian does not use the infinitive anymore. Davai, Dai, etc are conjugated forms.

There’s a grafitti on a garage door close to where I live which says “Sakam da se izpenyavim”. You don’t have to translate that, just for reference. A guy from Varna may be a little puzzled by that, but in Sofia the meaning is well understood.