Let's see if i understand correctly the card usage..
In a game turn i can play as many card as i wish as long:
1 i have the card in hand and enough resource to burning

2 between two unit activation i can play a strategy card. If another strategy is in play, that first one is discorded. If i play a strategy, then my opponent can play a strategy that discard my strategy card and stay in play up to the control phase or up to the next activation unit where i or my opponent can play another str. card which discard the last one played. Between two unit activation both player a and b can play once a strategy card
Which, if played as second let you discard the first card played.

3 i can play a tactical card between two single model activation of both player.
There could be only 1 at game turn on a single model/squad, but i can play many at the same time on different target.

4 gears card. Can those be played any time and i can have Max 3 at the same time in play.

Is all that correct?

1) Yes, as long as you have the resource cards available you can play any of the cards in your hand.

2) No. Strategy cards are only played at one point in the turn, at the end of the control phase (see flowchart on P.51 for when this occurs). As there can only be one Strategy card, the player with the initiative can play a strategy card and prevent the other player from playing theirs. If the player with the initiative does not play a strategy card, the other player(s) will get the chance to do so.

3) yes, tactical cards can be played between individual model activations. That means between individual models within a squad, or before activating a single model squad. The player with the initiative (i.e. the one activating this squad) can play their cards first (as many tactical or gear cards as they like, as long as they have the resource cards to pay for it). Then the other player may play as many tactical or gear cards as they like. You can choose to discard a tactical card at any point in the turn (to remove the negative effects on your troops or the positive effects on theirs, for example), but otherwise they remain in play until the next control phase.

4) Gear cards can be played between individual model activations, the same way as Tactical cards. They remain in play instead of being removed in the control phase, and a max of 3 can be in play at any time. You can choose to discard any of your own gear cards at any point in the game.

1. Correct

2. See page 6 of errata v1.4: Strategy cards can only be played at the end of the control phas before any squads are activated. The player who wins initiative has the option to play a card first. If they do not, the other player may play one. Strategy cards are discarded in the control phase, so once one is played, it stays in play: you cannot force your opponents card to be discarded unless a card specifically states that it allows you to discard an opponents strategy card that is in play. An example is the Dark Legion card "Ripped from Reality".

Once a strategy card is played, it stays in play until the next control phase, or you play a card that removes the card in play.

3. Correct

4. See page 5 of the errata v 1.4 : theycan only be played between model activation phases of any player. The player that will activate the next model can play any number of gear cards on any squad (up to the 3 gear card limit) before the enemy player. Just like tactical cards.

Wraith beat me to it!