You don't have to further process the waste wood you describe to make it a usable fuel, it's already in a form that will burn quite well :-)
In essence if it'll fit in your stove you can burn it, although you can create pellets or bricks from chips/dust/shavings to help slow burning and maximise heat output. From reading around it would appear that most woodworkers who burn their waste don't bother but that doesn't mean anything. Whether this is worth the time and effort is an individual decision, and will in part be based on the type of stove used.
Also curious as to any woods that are naturally more toxic to burn (other than the obvious MDF, plywood, and the like.)
Whether to burn MDF and plywood scraps, or whether you can safely, in the woodshop is a contentious issue.
Some people do it but some won't, and while some who won't do not state why that is others point to the safety issue of burning the urea-formaldehyde glue commonly used to bind MDF and bond the layers in plywood.
If you look online some sources state you shouldn't burn this type of material because it will release toxic gases (principally formaldehyde) into the room being heated. But we're not talking about open fires, where you most definitely would not want to burn anything like MDF on a regular basis. Any stove properly made and installed is of course already set up to prevent smoke and gases from escaping into the room. So in reality the risk from burning this material in a stove (particularly a modern one) is not what it's often made out to be and it could be perfectly safe to do.
Now this is in relation to you in your workshop, but there is an additional concern and that's with what's coming out of the chimney or stovepipe. If your workshop is close to other people any toxins released in your smoke must be taken into account.
Good modern stoves re-burn their smoke and this may reduce emissions to acceptable levels but obviously you'd need to look into this further.
Capping all of the above, depending on where you live it may be illegal for you to burn this sort of material. This is something each person must look up for themselves as local regulations may apply.