On the crating. If he is doing fine with no potty accidents in the night, then let him sleep in his bed by you. I see no harm. I would always set up the crate (cover the top and 3 sides and leave the door open...just so he has a "den" to go to if he ever wants to "get away". Dogs love dens (this is why I actually use a blanket to cover the top and 3 sides of Mandie's crate...so it feels that way).
When you are away, I am one who doesn't think dogs should be crated for extended periods. I would highly suggest getting an xpen, instead. That way you could set up an area just for him that has his bed, food, water, pee pad, and toys.
On the neutering...be sure to get the pre-op blood work done. It's important for Yorkies and breeds that tend to have liver issues. For post-neuter, I suggest having some pedialyte and chicken broth on hand. Oh and a dropper/syringe (the kind for meds). The first day, he may not want to eat or drink but he needs to. If that happens, try feeding him his kibble by hand. If that doesn't work, drizzle some chicken broth over it (this worked for Mandie). Use the dropper to get him some water and mix in some pedialyte here and there. By day two, he'll probably be eating and drinking fine. OH..and just in case the meds get him constipated..have some mineral oil on hand. You can put a bit on his food AND rub a little on his bum.