If he uses a KYC exchange, even for small amounts, could authorities link his wallet to him?
Every transaction can be searched online. For ETH transactions you can use ethplorer.io to track it. If they care to track it will take them to finding the exchange used to receive the money. Of course upon deep research they can link it.
Could banks or tax offices freeze his account or ask for explanations if more money starts showing up?
This will depend on how the Germany account policies works. There are different tier when opening an account, higher tiers will receive higher amount that the lower tiers. Account freezing will occur if he uses a lower tier to receive an amount that is higher than his limit.
Would this be counted as "assets" and disqualify him from his student support?
This i dont know.