Toothbrushing has been an evolving thing with us and DS. When he was little (2 years old?) we gave him the toothbrush and said: "you can do it while we count to 10 and then it is my turn to do it for 10". He did always like doing the toothbrush himself so that helped. Now that he has gotten older he still does it himself but we tell him that mommy/daddy have to check his teeth. Something you might also try if you are concerned about dental hygiene is flossing. I know it sounds a little crazy but someone told me that they flossed their toddler's teeth by having them sit in front of them and the child lay their head back into their lap. I thought it was nuts until I gave it a try and he will sit there - we use a small stool in front of the toilet - and let us floss his teeth. I tell him little stories while I am flossing his teeth, he seems to like the closeness, and I feel less worried about how well we are brushing.
With the fingernails it seemed to help if I did mine first while he was watching and gave him the nail file to occupy one hand while I do the other.
Hope you find something that helps!