Let me try now,
"I intend to sentence you to a pecuniary penalty of 30 day-fines under suspended sentence of up to the maximum"
-I think "je me propose" is correct here and means "My intention is". As when you say "je me propose de maigrir" I intend to loose weight.
-I do think this is a judgement (a decision of a judge) only judges can impose those kind of penalties and only through formal judgements.
-You are right about "pécuniaire", it should be "une peine pécuniaire" unless it's some legal ellipsis I have never heard (as if "peine" was superfluous)
-A "jour-amende" is called a "day-fine" in English, as well as an "unit fine". It's a substitute for prison, that is, prison is avoided as far as the fine is satisfied. Every day-fine is equivalent to one day in jail.
-"Stay of execution" is an order to temporarily stop the execution of a judgement. For instance, in light of new evidences that could absolve the convicted, or for medical reasons. It's called "suspension de peine" in French. Execution is often resumed afterwards.
-"Suspended sentence" ("sursis" in French) is when the judge passes a sentence and at the same time suspends it during the same period of time the original penalty had. Throughout this period the convicted should show a good behaviour and commit no other crime, otherwise he will be called on to serve the sentence. Once this period is elapsed, he is free to go.
I'm sorry if I was too exhaustive.
CC: Francky5591