First one is a run-on sentence -- it's actually two sentences crowded into one. And what do you mean by "wrought"? It doesn't make sense in this context.

"I proposed that Mr. Hitachi be launched to the job. Only a veteran in this field can finish a wrought task."

Next one simply needs a preposition so that the object makes sense. "To it." The preposition needs to refer to the object in the beginning of the sentence -- you are not objecting to your boss, you are objecting to the powwow. You also need to decide whether the sentence is in the past or present tense, so that the verbs will match.

"When my boss proposed holding a powwow on the prairie, no one objected to it."

This last one is really complicated! For starters, it's a run-on sentence and really needs to be divided into two. It would also make sense to simplify the subject in the first half of the sentence; it's kind of convoluted. I don't know what you call the difference between "reposed" and "reposing," but you need to say "reposing." I'm tossing out "for the best" because it really doesn't fit and adds nothing to the sentence. Is your minstrel serenading someone *on* the balcony, or is he standing on the ground serenading someone else on the balcony? If he's on the balcony, then he is serenading "from," and if he is serenading someone on the balcony, you simply say he's serenading the balcony.

"I advised him not to serenade from the balcony. The neighbors were all reposing at that time."

You can also make this into one sentence.

"I advised him not to serenade from the balcony, as the neighbors were reposing at that time."

Whew. Check it out -- I'm a grammar maven.