Okay, Hold on. Does no one read what I write?
First, Mal goes first, beating even the boosters. This happens before Doom's character starts to draw her weapon. This is why we -have- init checks, so we can see what happens when.
So, Mal, first thing that happened was Jade did her talky thing. You started this a good couple seconds before Doom's character, because your init was nearly twice Doom's.
Everyone got that?
Now, if Doom wants Wrench to then draw and start things off, that's fine, but that happens in order of initiative. There is no surprise check here, so AS SOON AS things start to go all action-y, I check init for everyone. Boosters, guards, automated systems if any, etc. Typically in CP2020, we declare and carry out our actions, then the next person goes, etc.
With multiple actions and really close init totals, this gets a little silly, so I apply a little reason. No matter what, though, Mal easily goes first. Not tooo far behind her, someone else will go. Then, well, then we'll see. But Wrench is low on the init pole here.
And since Mal already declared her action, it will not be "following along". Your ""Whe... where's the stage? Do you at least have a karaoke machine?" happens before anything else. I just want to see what Wrench's planned response is - in other words, if she goes for the draw anyway or she gives it a heartbeat to see what happens before doing so.
Lastly, I favour a "realistic" approach to combat, which I will explain as we go and allow retconning. One example of this is that just because it's your turn, if you spend your full movement charging towards someone who has a weapon out and pointed, yes, they will get to shoot at you out of their turn sequence. Unless maybe you're crazy fast...anyway. If you don't have a weapon drawn, different story.
You can of course move and shoot - in fact, you can do anything you can do in real life, plus extra. It'll cost you negative penalties, is all. -3 for each additional action beyond the first, cumulative. Further penalties if you're running.
Oh and semi-auto weapons can fire up to their maximum RoF per attack action, ( and you can do multiple actions in a turn), whereas full auto, that RoF is your maximum for the whole 3.2 seconds.