If this SSD to my old maternity ward?

Yes.
All work fine, and will work perfectly.
SATA 2.0 does not affect the operation of the SSD will work no worse than SATA 3.0 solutions.

The only unpleasant moment of your Mat. Board likely does not support AHCI and the drive will work in IDE that doesn't support things like NCQ, and TRIM.
Therefore, to drive work efficiently it is necessary to leave the reserve - over provisioning? Do it best utility from the manufacturer.I would recommend 30-40Gb left in the reserve.

1 -

Board probably does not support the AHCI interface

according to generation, the Board certainly supports AHCI. but the correct answer is you can only find in the options of the BIOS. Windows 7 should definitely be installed when you select options (although there are instructions on how to prepare it on a live system, to change the options. Google to help). Windows 10 is likely to be able to adapt on the fly (without guarantee)
2 - the interfaces are completely compatible. just speed will be at the level of smaller (SATA2). but will load it to the limit. here a miracle is impossible. but not the fact that budget SSD with SATA3 has a maximum speed SATA3. so maybe the loss will be very small