I'm using grbl to drive my PCB-making CNC too, but that's where the similarities end - I don't use EasyDrivers, limit switches or probing, so there's not much I can help you there with. Two pages related to wiring up and configuring grbl you might be interested in are
this one and
this one - by the way, you switch wiring looks fine. As noted in the linked page, your probe goes to the A5 pin, just as if it were another switch: it just senses contact between your PCB copper and the tip of your tool. To use the limit switches, you'll have to enable them in the grbl settings - see the linked wiki page for details (setting $21 and thereabouts). To use probing, you should only need some piece of software that knows to send the right probing G-code command to grbl. Again, I don't have first-hand experience with any of that.
Regarding heat, my drivers are older TB6560 chips which do unsurprisingly heat up, but they have a heatsink to match and a small fan for the whole box. No idea what's normal for Easy Drivers, but at any rate heatsinks are a good idea. You could limit your idle waste heat if you want by connecting your stepper driver's enable pin to the appropriate grbl "enable" outputs, so motors don't eat current when they don't move. However, that would also mean the don't "hold" the relevant axis and there might (or might not) be issues related to how fast the enable signal gets sent and processed before a new move, so you might not want to bother with that. Personally, I used not the enable input of my drivers but their current selection pin (which your drivers don't seem to have) for the same purpose, so my motors still "hold" when stationary just not with full current / torque.
Personally, I'd go with ball screws all across the board - I'm not saying you won't be doing 0.65mm pitch PCBs, but I am saying you'll need any and all help you can get for that sort of precision - I never went that far. Good luck!