Using a crate will slow down toilet training. They learn [ sometimes ] not to mess in the crate but then see everything outside of the crate as the place to go so you still have to do the basics anyway of considering feeding times related to toilet needs, spotting the first sign of when they need to go and acting on it, rewarding after they have been, not during [ as it can distract them into stopping the flow as it were ].
Best way as far as I`m concerned is ignore all accidents in front of pup, clean up without a fuss, place it outside in a spot you would like pup to use, next time pup looks like needing to go pop on a lead, take pup near to where you put the previous lot, let pup get the scent [ dont march pup up to it ! ], let the scent trigger the need to go again, praise/reward. Before long pup will start asking to go out. My average this way is 4 to 7 days for any of mine and past fosters to get the idea.
Re eating it, there are many reasons, for some its food deficiencies, for some it`s what`s coming out still being rich in food content so is appetising to them, for some it`s habit, but for most it`s a instinctive behaviour to hide it, especially any dogs which have been told off for an accident - or perceive a telling off - even an owner just sighing in frustration can cause this hence it should be cleared up preferably without the dog seeing it being dealt with. I suspect many dogs which are thought to be clean in their crate are as likely to be eating it either to avoid reproach or so they don`t have to be near it when they can`t escape it.
I would suggest using the crate as a bed/den so that should pup ever need to be exercise restricted or be afraid of anything like storms and fireworks so that there is safe place for pup to go into by choice but for toilet training you would be in for a much longer road than by not shutting pup in overnight.
Where does pup sleep at the moment ? My crew past and present, including fosters and friends dogs, have always always slept with me whether in the bed or the floor so when they needed to go they could let me know, though it was very rare that they needed to as they have tended to through right from the start because they were so relaxed by not being alone - don`t forget if a pup sleeps alone shut away from their human, just waking up and feeling so alone can cause a stress reaction which can result in toilet accidents and can become a hard cycle to break. If you don`t want pup on your bed then fair enough use the crate in your room so at least if pup needs to wake you it gives you the opportunity to keep consistency going for acting on when being asked for toilet time.