Europe is a big place, but my understanding is that the US is the outlier here and Europe is relatively similar in this regard.

The only time I really saw checks used was when I was a child ~30-35 years ago and my parents used them. I did once cash a check from an elderly relative, but that was very unusual and only happened once. I didn't even know it was still possible to do that, my reaction was more like if someone had handed me a stack of punch cards to run on my computer.

There hasn't been anything an average person used checks for in the last decades in Germany. Except a few elderly people, nobody uses checks and there are no rebates via checks at all.

The last few manufacturer rebates I have gotten come in the form of a pre loaded Visa card

I am in the UK and I have received two cheques in the last year, both for small amounts.

As it turned out, my bank rejected both because they were made out to [middle name] [surname] rather than [firstname] [surname]. Ironically the former is unique (probably) whereas they had another customer with the latter.

To receive money from someone you can just give them your bank account number or if you both have Vipps or similar just your mobile telephone number.

Granny can always give you cash or just send it directly to you account in the same way.

Cash is still fairly common, and manufacturer rebates are basically not a thing. If they were, you'd send them an account number (IBAN = bank ID + account number at bank) to transfer the money to.