Welcome to this site - great to see the smiling pic of both of you!
What kind of food do you recommend?
My thoughts are (a) get a better quality kibble and mix it with bits of chicken (meat only if cooked), cooked liver, kidneys, chicken giblets, raw chicken necks etc. If you are keen enough you can try feeding raw.
Treats, toys, shampoo?
For treats you can give bits of cheese or liver. Cheap toys our boy likes are stuffed animals (you can get cheap from local thrift stores, salvation army stores etc), and he quite likes playing with plastic bottles. Remove the eyes off the toys and also remove the cap off the bottle.
We don't use any shampoo. Our boy goes to the beach every week and also goes to the streams once or twice a week. So we only wash him about once a year.
What kind of solution to use in his ears?
We don't use any. I have been thinking about using some flea treatment called revolution instead of the advantage we have been using as that apparently deals to ear mites also.
He doesn't let me near his tail pocket, no matter what I do. Got any remedies that work with your dog, when he won't let you touch his butt?
It may be he has sore anal glands, so those might need to be expressed. I think most bullies love to be rubbed on their butt - just do it gently when he is relaxed. But it may be that he has some sore in his tail pocket, so I think you need to check this out.
HATES a bath, how can I make him fight less when in the bath?
We've always made the bath a pleasant experience eg made sure the temperature is nice (bulldogs feel heat more) and don't force a full cleaning if he doesn't want it. I think you have to take it slowly eg with a pool/bath outside and not force it otherwise you get fighting resistance.
I've noticed his collar has rubbed the hair off his neck, would you recommend a harness, or anything else?
We take our boy's collar off on the weekends. A harness is probably better but it is no big deal.
What to use in his eyes? How often?
We don't put anything in our boy's eyes. I would only do this if he had dry eye or something.
How often to put vaseline on his nose and face flaps?
It's really important to wipe their wrinkles regularly. You might be surprised if you look carefully how many wrinkles there are. I would do this at least once a week, but even daily if necessary.
He humps... ALOT. Is neutering going to stop this completely, a little, or not at all?
At his age it won't help in my opinion. We have a big dominant boy VERY interested in female bullies but he very rarely humps. We give him a lot of exercise (total 3/4 hour a day walks in the weekdays and 1 1/2 hour walks or more in the weekend days) and also as soon as he starts showing signs of humping we tell him no.
Best of luck with your new arrival!