While I do not trust the Huff Post and those other networks, it is true indeed that he would have only been able to do this with the support of those "hawks". I would still say it was justified though, considering Soleimani was actually in Iraq for the sole purpose of causing unrest.
I think basically what happened was the hawks were already bloodthirsty and then the Iraq attack happened. So Trump ordered the hit and they allowed him to. I don't believe this is related to the impeachment, since causing a new war could ruin his chance of winning.
While this is something that could've been true. I highly doubt that Trump would've been able to convince military generals to go alongside this if they thought it was just a political hit. Soleimani was someone who killed Americans, and was most likely planning the death of many more Americans. Pretty sure this is what was going on.
Trump had caught wind of all of this after Iran had killed a US contractor.
While yes, at the end of the day Trump gets a political win from this. But first and foremost this is a military and strategic win.