You can save game by pressing down when on flame-like spots (not the ones that hurt you, these are spikes, but the ones with pixels going upward). Also, touching these spots will heal you, but to save you have to actively press down (I did it that way so a player can make a choice whether to save on that position or just heal).
For menu, P or Enter on keyboard, or Start or L1 on gamepad will toggle between showing the menu and not. Use direction input to navigate and jump key to use any menu function. Hope that helps. :)