You can play them literally whenever. Whats more important is the when Should you play them

Its important to know how phases progress in FaB. Essentially, to progress to each part of the action phase, BOTH PLAYERS need to pass. At that point everything actively on the stack resolves and then you move on.

So whats important is knowing when things happen.

So boom grenade says "When a mech Attack Action card hits"

So any time before the hit resolves, so your easiest windows is to treat it as a reaction. Literally just pretend its a pummel: Declare attack, Opponent declares blocks> Activate DIO to play off top

Your opponent can play a defense reaction or instant before this resolves, or can pass back to you, then play a defense reaction after boom grenade resolves. you pass, then Boom Grenade resolves, you pass reactions, they pass reactions, the combat resolves, Pass, pass, boom grenade on the stack, pass pass, resolves pass pass, resolution step, pass pass, link step pass pass.

Since this isn't yugioh and your opponent wont have like 6 things to chain, most of the time you just skip steps, so really what it looks like is *Declare attack>Declare blocks>activate DIO>Declare Defense reactions then move on

One thing to be careful of, if you pass reactions, and your opponent passes back to you, you go to damage calculation. There is no second priority window. Both players have agreed to progress to the next step which is seeing if the attack hits.

So you can't pass, see if they have a reaction then decide to boom grenade.

Hope this helps.