I have a Mac mini (Mid 2010) with 2.4 GHz CPU and willing to upgrade its HDD to SSD.
Can I use a sata3 SSD for it?
Yes, you can.
Here are the theoretical bus speeds
SATAI - 150 MB/sec - 1.5 Gb/sec SATAII - 300 MB/sec - 3 Gb/sec SATAIII - 600 MB/sec - 6 Gb/sec
In theory, a very fast drive could saturate a SATA2 bus, but if it does, it will still send the data, just slower than it's capable of. If that bothers you, just buy a slower SATA2 SSD drive.
Regardless, you'll be very happy with the performance upgrade over a slower drive. It's the best upgrade investment you can make.
SSDs with SATA-X are backward compatible.
I for example use a SSD with a SATA3 capability on a SATA1 bus. (Crucial m4 in MBP 3.1)
My advice: Always take the latest SSDs. They have a more refined garbage collection. It's also preferable to take a SSD with SATA3 in order to profit from the faster bus speed in case you use the SSD in another computer some day.
Nope, because SATA3 in a Mini began with the 2011 models, or with Core i5/i7 processors. The SSD would saturate the SATA2 bandwidth, but I don't see why you would spend more money for the little extra speed it's gonna give you. Stick with SATA2 SSDs is my advice.