I was born and raised in Europe, and I live in a European country. But I do possess a dual citizenship (with a Hong Kong ID card and Chinese return home permit). I plan on going to China for a month this summer for a scholarship. Will I need to get a visa or will my Chinese return home permit suffice? Do I need to be careful with anything?
No, you can NOT enter the mainland of China as a foreigner if you are a Chinese citizen. Chinese nationality law is complicated because it applies differently in the mainland and in HK/Macao. I'll try to explain.
The 1980 Nationality Law applies in every part of PRC, and dual nationality is de jure forbidden in the PRC. If you are a Chinese citizen born with dual nationality, you must renounce your other citizenship (or Chinese citizenship) when you reach the age of 18.
However, since you are born to a PRC citizen who happens also to be a Hong Kong permanent resident, the law applies differently to you. The enforcement agencies in the mainland and HK interpret the law differently. In practice, Hong Kong permanent residents with dual nationality are not stripped of their Chinese citizenship unless they personally request so. So, while no one will ask you to renounce your other citizenship, your dual nationality will not be recognized in China.
By HK Immigration Department regulations, you CAN enter Hong Kong as a foreigner, and you will be treated as a visitor. If you do anything other than hanging out, though, you need to enter as a permanent resident.
If you want to enter the mainland, though, you must use your Home Return Permit because you are a Chinese citizen. No exceptions. Well, if you can cover up the fact that you are actually a PRC citizen, you might be OK getting a visa. But then if they find out you're a Chinese citizen I don't know what will happen to you. Chances are that, since you have a Home Return Card, they already have your name somewhere on their database.
So, the answer is: you should enter with your HKSAR passport and Home Return Permit.
But another note here. Not all HK permanent residents are Chinese citizens. Technically only those Chinese citizens should get Home Return Permits, but this does not seem to be the actual practice. So, you might actually not be a Chinese citizen, but your Home Return Permit should always suffice.