I want to have simultaneous action selection, but the action selected may need some additional information, like the space on the board that it is of relevance to, additional equipment that you choose to use or have to use, etc. How can I have all players select their cards without giving away that they selected a certain type that would require additional cards or information, or even how many additional cards are needed? I want to prevent the players from being able to alter their selected action in any way by/after getting additional information. Feel free to replace "card" with any other token.
Most games that let you select a variable number of something in secret, will either give you small tokens that you hold in your hand, or by giving you a screen to hide items behind. Some also give you duds that you can place instead of something useful, to bluff about what you're doing.
For example, Shogun lets each player pick an action for each province they have. Each action can only be picked once. What they do is give the player a card for each province they own, and they put their province face-down below the icon for the desired action.
When you want to expand this mechanic so that you can select additional options, you could for example slide additional cards under that action, then give each player a few blank cards that they can use to bluff about where they are taking serious actions.
Alternatively, if the players take one action at a time, it's easy enough to just give them a screen. They put all the stuff that is used in the action on one side, and everything else on the other. That lets them completely hide what they are doing from everyone.
Some games also do the same thing, except they use a bag. This works really well with tokens; you put all the tokens you want to use in the bag and the rest you keep behind your screen. Or you can use a dial for selecting amounts (used by many games).
Take a look at Waving Hands, found in a comment on the RPG SE. Two (or more?) players are dueling wizards, using hand motions to weave spells and/or stab each other. Each turn, each player writes down on a piece of paper their moves for the turn, then they reveal their actions and everything happens simultaneously.
It might be as simple as having pen and paper on hand, or erasable writing space on cards, to write down the target of whatever item you're using.
It's not simultaneous, but you might be able to find some more ideas from looking at Escape From the Aliens in Outer Space.
One more good example of simultaneous selection with additional information is the combat system in Scythe. Players use a numbered, cardboard wheel to indicate their base combat level, and can (optionally) include one or more cards to increase their combat number. Players have no way of knowing if you are playing cards, or how many, as they are blocked from view by the cardboard wheel.