It may be a wolf spider, or even a brown recluse. The brown recluse spider can be deadly to pets and also humans under the right circumstances. Do a search on the internet for brown recluse spiders, and there should be a picture of one with a full description of the poison they produce and the damage they cause to the skin. Can you see the area where your dog may have been bitten? Possibly your dog got bit on his mouth area. Wolf spiders usually don't produce a deadly bite. I'm sorry to hear about you dog.
Not unless it's a brown recluse and then it's very possible.
If a brown recluse bit your dog ... There is no possible way to not notice. No matter where it was bitten it would be seen as soon as a few hours .... A dog could have died suddenly from anything. Dogs, no matter the size, are all capable of suffering from a number of ailments that are not normally associated with anything other than humans. Heart attacks, stroke, liver failure, and a number of other things. But, if it was a spider bite it would have been noticed somewhere way before the dog passed. I'm sorry for the loss of your dog btw.