According to these, If I use an order and declare Suppressive Fire with Puppetactica Company which contains a Master and 3 puppets with marksman rifle, will all of them enter Supp. Fire state?
Yes, but the relevant rule governing this is a bit further up in the Peripheral rules: ► Peripherals are always activated with the same Order as their Controller, executing the same Short Skills of the Order, or Entire Order, although they are not required to have the same target.
Note, you can also do this with a Command Token if you are going second. Definitely the best Suppressive Fire roadblock out there to prevent alpha strikes.
it's unclear. the rule states that when a skill is declared that requires a target, only the controller and spearhead will perform the skill. Suppressive fire does not require a target so... I would say they all go into supressive fire.
If the Peripheral and Controller declare Move, what happens? They all perform the skill because you default back to the main Peripheral rules. The same thing happens for Suppressive Fire, because the exception specified in Peripheral(Control) doesn't apply. The "Attack" label on the skill really just ends up doing things like triggering the cancellation clause of various marker states (the whole "declares an Attack" business) and the like.
It's actually a lot easier than that to clear this interaction out, see below underline emphasis: https://infinitythewiki.com/index.php?title=Command_Tokens One Trooper from that player's Army List can activate the Suppressive Fire State (along with their Peripherals, if they are a Controller), following the Activation rules of the State.