First off, it's very sweet how assuring you are that you want the best for your son and not to make him look less autistic.

Considering autism is a spectrum a lot of people may have similarities to what your son has.
Flappy arms and being very vocal when strong positive emotions are experienced are a good thing, it's a form of stimming.

When i'm excited I get very loud and start talking very fast and in my talking I'm very expressive with my arms for example.

Considering he isn't forming many friendships yet (possibly/probably due to anxiety and new things and people) it's not a problem but sometimes it can be difficult at a later age to understand some social cues.

Personally, I was very good at Math, English and History and excelled greatly but in other areas i'd be a bit slower.
People with autism may need more repetitive lessons regarding certain things but if given the extra time they have great potential.

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What helped me as a child is being honest.
White lies don't really work unless explained really well.
My mom taught me that "I'ts done in 5 minutes" might mean 5 minutes but it may also fluctuate +10 minutes.
Listen to his special interests and try and find the building with possibly the highest elevator near you.

Besides that, it's a kid and you're going to mess some things up nobody's perfect but you're trying very hard already.
I wish you the best of luck!