Hello, there.
Which version are you using? I assume the PC version. To use powerups press E, the shield icon changes to the mode you are in, and pressing the firing button "left mouse" executes the action but it takes energy, which can be replenished by collecting 'batteries'.
The player walking speed is set for a reason. Any faster and the player will reach areas he is not supposed to, through jumping.
Some areas you say you cannot reach means you cannot reach them yet
The mechanism to posess animals and the Wizard tent on the 'leafy manour' level are probably bugs, which we have just fixed.