Just make sure he is reaching his milestones.
Raise any concerns you have when you see the Health Visitor/Paediatrician.
He is just at that age when he should be becoming more social.
The things you mention are on a scale. All kids can do them, they are not an indicator of autism by itself. My son rarely flaps or toe walks, infact I have seen perfectly typical kids demonstrate more flapping/spinning/toe walking than my son.
From your post I just don't see enough stuff to make me wonder.
He sounds like he is chatting and interacting with you which is great.
No idea about the blanket and pelvis grinding. Guess he must just like the sensation.
arm flapping is just a sensory stimulation. Many kids do this. If he is talking and interacting with other children socially, I wouldn't be concerned. You could always bring up these things with his pediatrician. I think you probably already went in for his 24 month checkup and the next probably isn't until 36 months? You could always make a phone call or ask the questions during his next sick visit if he has one in the next couple months.
Reading your post your son sounds like a normal 2 year old he is doing all the things 2 year old do, what is it you are worrying about,a lot of children Flap thier arms and tip toe ,its a game , if there are other persones making you feel there is something wrong and it has made you anxious ask your Doctor , the laying on the floor could he be copying another child he has seen do this. Enjoy him.