Would the Hunnic tribes stopped earlier from causing massive destruction they did in OTL and instead assimilated as law obeying citizens of the Kushan Empire?
For the Kushan Empire to last until the times of OTL's Sveta Huna invasions, it would have to be a truly long-lived Indian Empire. What could cause this?
Either way, if it remains stable, then the Hun challenge is already fulfilled. If we follow the hypothesis that the Kidarites and Hephtalites both originated somewhere between Sogdia, Kashgar, Kashmir and Bactria, and the Kushans maintain peace and stability there, then there's not going to be any Sveta Huna invasions.
Islamic expansion stopped at the borders of mid Iran?
With such an early PoD, Islam is not a given. If the Kushana establish a firmly Buddhist empire, they could renew Buddhist missionary activity Westward, too, like in Ashoka's time, and with strengthened Buddhist influences in the Arabian peninsula (most likely its coastal fringes), the religious makeup of 7th century Arabia is so altered that I'm not sure Islam must arise.
But if it does, the big question is how Sassanids and Kushans will have coexisted over centuries. If they warred all the time, which I suppose they might have - which would have interesting implications for the (Eastern) Roman Empire -, then maybe the Caliphate's attacks on the Sassanids are supported by the Kushans at first. How things would turn out later is a different question and depends on lots of details.
How would they behave with the Sassanids and the Byzantines/Romans? A Zoroastrian survival?
Yes indeed, the former is the big question. The Byzzies are too far away to matter for them. The Sassanids are certainly weakened by having strong empires surrounding them on all sides (except for the steppe which isn't much better as a border). Zoroastrian survival is not made likelier at all.
How would Indian religions look without the Islamic invasions which caused the hardening of Hinduism?
First of all, we need a reason why the Kushans are so strong and stable over such a long period. It requires both structural reasons and cultural cohesion. For the latter, the only option I see is Buddhism because it's already been around in all the places mentioned and it has had a history as an imperial religion already, so the Kushan Emperors might style themselves as restorers of Ashoka's old glory days. That could mean Buddhism forming an umbrella over all the various Hindu cults. Some groups might insist that Buddhism is Nastika, and harden in opposition to it, but many more Indians would simply both worship their deities and the Buddha...
How would China and Mongolia do?
"Mongolia" is still a backwater in the 1st millennium BCE, first as the heartland of the Rouran, later as the Eastern part of the continent-spanning Göktürk Empire, if this one isn't butterflied. It might well be because the Silk Road which it controlled IOTL would be Kushan-controlled ITTL, unless you posit that Turkic nomadic attackers pry away parts of the huge Kushan Empire over time in the North. Other than that, China would be linked even closer with India.
How would the ethnic makeup of India be?
That depends on what happens after the fall of the Kushans, for at some point, they must fall, like all empires do.
IOTL, we do not know much about the change of the ethnic makeup caused by Kushan rule.
Tocharians survive and are integral in Central Asia and India?
They survived IOTL way beyond the limit of how long a plausible Kushan Empire could ever last anyway. But if a large Tokharian-language Buddhist canon exists alongside Pali and others, it could indeed remain a prestigious language over a longer period of time. Or, it could be replaced earlier if the continuity of the Kushan Empire and its official Indian-based Pali canon mean that the Tarim Basin Indianizes culturally and linguistically.
Since Mughals and British cannot touch such a powerful country
Wait, we're really entering ASB territory now. That's way too long. (And even if it weren't, then at least both Mughals and British would be butterflied.)
PS: Please keep political correctness out of this thread.
I don't know what you want to say with this, but I think I don't like it.