Do I need a proxy for Instagram?
Only if you are changing where your traffic appears to come from. If the device is a real phone on a real mobile SIM, there is nothing for a proxy to fix — the traffic already originates on a mobile network.
Are mobile proxies as good as a real SIM?
They are the closest a proxy gets, because the address belongs to a carrier's pool. But it is still a shared address, still a hop in the path, and still only the IP that changed. A SIM removes the need to mimic anything.
Why do datacenter proxies cause problems?
Because the address is publicly registered to a hosting provider, and ordinary people do not browse social apps from a data centre. It is the easiest category to identify. It is fine for scraping public pages and poor for anything attached to an account.
Is a VPN the same as a proxy here?
For this purpose, close enough. Both route your traffic through somewhere else and change the address it appears to come from. Neither changes the device.