I’m definitely no expert (first CNC cut for me was just a few weeks ago 
), but from what I can tell, if you’re using MeshCam to generate your toolpaths, you would have to make a new model with just the pockets and holes (and not the rest of the shape modeled out) so that MeshCam only tries to clear those pockets and holes. i.e. just trick it into doing what you want: if you have a super complicated shape but just want to mill out 1 pocket and a hole, just create a model of a rectangular block with a pocket and a hole in it and give it to MeshCam so all it tries to mill out is that pocket and hole. Alternatively, give the full model to MeshCam but use the “Set Machining Area” option and make it only mill out the sections with the pockets or holes by defining machining and keepout regions.
Yes, you can set drilling operations in MeshCam, see here.
Alternatively, you could try using another CAM program - I started using Fusion360 (free for hobbyists, and imo pretty nice for modeling as well), and it has options for rest machining, where you can give it a model that represents what your piece already looks like, and it will only generate toolpaths that take it from that model to the new one (so you can give it a model of your piece minus the pocket and hole, then a model of the piece with the pocket and hole, and it will only mill away the pocket and hole).
It also has a lot of options for specific drilling operations with control over the toolpath strategies. Not that I know the differences between those strategies, but you can change whether it goes straight through or if it goes down a bit and then comes back up to eject chips before continuing, etc… It also has options for tapping the hole, but I’m not sure our spindle has the horsepower to do a regular tapping operation. I’m doing some research on this right now, but it looks like the other solution would be to do threadmilling, and I actually just posted a question on it a few hours ago. I’m pretty sure it can do threadmilling; just not sure of the exact details of how to do it yet. You can follow along and see if anybody more knowledgeable chimes in here