what would you say this is?

[bananasplitwithcherry]

If a child shows the following behaviours/traits what would you say is going on and what would you suggest in terms of investigation / action?
Has involuntary / habitual movements (tics?)
very sensitive to noise (wears ear defenders in noisy environments)
has very fixed ideas / likes routine - e.g. insists on having the same meal in the same place on the same day. can have a meltdown if they don't get their own way or if the routine is changes
repeats certain phrases over and over, even if asked to stop.
speaks very loudly / no "indoor voice". doesn't adjust volume in response to social cues
academic ability significantly above age (maths farthest ahead)
but consideration/manners/empathy generally lagging behind age - has no filter and can say things that most kids their age would know are very rude.
Slow to make friends but fairly unconcerned about not having friends.
All these traits have been present for at least 3 years.

Nobody can diagnose over the internet but a lot of those traits are present in children diagnosed with autism.

I would start by talking to the GP, and assuming the child is of school age, to the school SENCO.

Thank you. that seems likely to me too. Any ideas about the repetitive movements? I have come across these possibly being discussed as "stereotypies" or "stimming" , but it is new to me. Seem to be classed as distinct from tics. And the repeating of phrases as "echolalia"?

Yes I'd say ticking all the boxes for ASD there. Stimming is common with ASD, it's often soothing if they are feeling anxious - NT people stim too, ie pacing, tapping a foot etc.
Echolalia is the repeating of phrases picked up from other people or tv, they often have a message, for example the child might say a line from a tv show to indicate they would like to watch the tv show or they might say 'bad dog' when someone is behaving badly because they have heard those words used with bad behaviour. It is a stepping stone in learning language. I've read that while NT children learn one word at a time children with ASD may learn differently and learn phrases that have a meaning for them although they don't understand each individual word within that phrase.