Is there a chart that tells the intensity scale or somewhere to look to see how we get intensity?
Not at all. Here's the setup:
1) You have a character. Your character knows one or more actions, which are built from components (effect and intensity being two of them). Once these actions have been built, what they do and how they work are set in stone. You cannot change them on the fly as you might with a mana system.
2) Your character can learn any number of actions, although the actions available to you will be restricted by your class choices. You can only prepare a certain number of actions at once, however. For example, if you're a 7th-level monk, you can prepare seven monk actions at once. You might prepare one Nerve Pinch (single weapon strike, "Sleep"), one Goky? Focus (self, "Hone Three", one encounter), one Mushin No Shin (self, "Rouse"), two Cripples (single weapon strike, "Maim"), and two Brutal Attacks (single weapon strike, Weapon Damage + 30). This is probably a small subset of all the actions you know.
3) Once you expend the actions you have prepared, they are used up until you refresh them by resting. More powerful actions take longer to refresh. For example, Nerve Pinch in the example above would be an adventure action at 7th level, so it would take 10 minutes of rest in order to refresh. All of the others would be encounter actions, so they would only take one minute of rest to refresh. Other possibilities include daily actions, which only refresh at dawn, and collaborative actions, which are like dailies but require several characters to perform.
4) Once your actions were refreshed, you could refocus to change up the actions you had prepared. Basically, you concentrate for 10 minutes, erase the numbers next to the prepared actions on your character sheet, and put in new numbers next to the same or different actions. This way, you can have a lot of different options available to you without having all of them available for use at any given time. This helps keep the game balanced.
Hopefully this clarifies your question. Granted, it's probably a lot different than you're used to, so read through the rulebook and give it some time to sink in. If you have any more questions after that, please let me know.
Can you refresh your encounter actions while employing an ongoing action?
For instance, can a healer use a Feign action, a rogue use a Vanish action, or a Druid be in a shapeshifted form while they attempt to refresh. If yes, what does that mean for the action in progress, ie. does it get refreshed or is it still considered spent?
You've got the whole "Detect Loophole" action down, Jessi. ;)
Generally speaking, there's no such thing as a sustained action, only ongoing effects. For example, someone else can grant you Feign, Vanish, or Shapeshift with the right action. Even when you're performing the action, then, you're simply creating an effect that is self-sustaining for its duration thereafter.
Keep in mind, of course, that Feign and Vanish specifically bar you from performing most actions, even common actions like resting. So, if you attempted to rest, the effect would end by default. This isn't the case with Shapeshift, so you can rest to refresh the actions of your shapeshifted form assuming its duration isn't up.
Class (like monk) determines what kind of effects you can use to build actions. Intensity modifies the effect. Thus, there is no "monk intensity," although there are different intensities which apply to effects usable by monks. You can read more about it under Components.
To get an idea of how intensity changes an effect, you have to see the effect entry itself. Thus, monks are able to use the Strike effect, which increases the damage of their unarmed strikes by five per point of intensity. Violent Attack is an action that uses that Strike effect at four points of intensity, so it increases attack damage by 20.
Hopefully this helps. Let me know if you have any other questions.