it is lottery. so it means, that you may not ever win until end of your life. considering this, your calculation is pretty much useless + you have to buy RPi and HDD and provide internet connection.
not just in datacenters but everywhere, because there will be reason, so far and don't see any except "good feeling" and this is wrong.
Many have raspberry Pis lying around and HDD too. I don't see much problem in using those. IMO $0.5 per month is very low given that many people already have high unused/unlimited bandwidth around the world. Consider lowering the max peers if you don't want to use too much of your bandwidth.
simple answer: to support the network.
it is better to run the Bitcoin core on a VPS instead using your personal hard drive. it really could kill your hdd when bitcoin core running for a long time.
yes, but there is any VPS out there with unlimited network bandwidth and at least 60GB of high I/O storage, which can be covered by 0.5$ per month? (let's use this calculation..)
if you are volunteering and support good think, you usually receive something as gift. from t-shirt and stickers to some discount or something. but doing this "for free" and donate it from own pocket is not sustainable at all..
I don't see much use in getting a HDD as it is different from SSD and high I/O wouldn't kill it. Unlimited bandwidth isn't needed unless all the peers in the world suddenly connect to you. I wouldn't consider it volunteering if I'm receiving something in return, I'm not trying to earn anything, I'm trying to support the network. Who is going to pay the T-shirts, stickers or discount in the first place?