Questions about strategy cards and their timings.

As far as I can work out they can be played at anytime to either cause an effect or as a response to an enemy model activation or your opponent playing a strategy card. Is this correct?

The only rule seems to be the player with the initiative is allowed to play strategy cards first?

If as the highest initiative player I chose not to play a card, then my opponent does, can I want to react by playing a card even though I declined to play one first?

In our first game, I had the Combi-Stick Predator on a tile with an Alien Infant and a Stalker. At the start of the game turn my opponent (higher initiative) played a card on his infant, I reacted by putting a separate card on each of his models that reduced or ended his activations. This happened before anyone even moved a model, is this correct?

Thats the way im playing it. It means there is a spat of card playing at the beginning of the turn, then the odd one when opportunity strikes. Ive tried playing the cards only when a friendly model is activating and about a third of the cards become pretty useless. I think the game plays faster and smoother with the cards being used freely which makes the game better for me.

The rules are pretty clear on this one (page 10):
Cards may only be played between model activations (unless stated otherwise on the card).
The player which activates the next miniature goes first to play a card.
(that is not the player with the highest initiative, but the player who will be on after cards are played!)

In my opinion there is no neutralizing of other cards by playing cards on top of other cards.
A card may be played by the player who is on, the effect is resolved, then another card may be played if anyone wants to …

Does that sound practical?

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There is a predator card "Missed Opportunity - Target model instantly deactivated"
It is not stated on the card, that you can play it at other time than between model activations.
But it doesn't make sense to play because between activations there is never any model activated.
This is the point I got all over this game. It formulates many rules very unclean.
You are left alone to make some sense out of it. Better would be to have more precision with language.
e.G. The addition "Play after an activation or action of any model." would be just the sentence I miss on this card, dear game designers!

No, I might want to play the card to make sure you don't activate someone later on. The card just switches someone off, doesn't have to be the model currently being activated (if that was possible).

I can - for example - use it right at the start of the game turn, before you can use your smartgunner that has LOS on one my guys. Letting you pick a model to activate, and then turning it off would be very powerful, because it would also make you miss your activation order. Instead of Alien-Marine-Predator-Alien-Marine-Predator etc... I could shut down the Marine you picked to activate first this Game Turn and you're now looking at Alien-Predator-Alien-Marine to start the turn. This way I shut down one Marine, and you simply pick another Marine.

Letting you use any card during the activation could open a load of trouble... strange interaction during the multi-step actions (Close Combat and Ranged Attack-Combat-Whatever).

As for the rule text... I'm with you. It's horrible. I'm done mentioned that since no one intends to fix it. I'll just fix for my game group and move on.

I disagree on the de-activate card, i use it to de-activate the model the enemy player is just activating. Yes its cruel but its also rare. I think of this as the model being distracted at the crucial moment and losing his/her go.
As they say "**** happens!"

Your two answers tell me that this card text is a missed opportunity of good game design.
We read the card and don't know for sure, what the author was thinking. :/

Perhaps the card text could be: "Target model instantly gets an activation token. It may not perform further actions this turn. Play at any time, even to interrupt an unfinished action."