A clone utility should be able to do the job.
If you reinstall windows on the new sshd, remove the old HDD during the process or windows will place hidden recovery partitions on the old HDD making it difficult to ever run without it.
Your key is tied to the motherboard so no reactivation will not be an issue.
If you are buying a sshd for speed, yes, you will get some improvement, but not usually much.
The nand capacity on a ssdh is not enough to be truly useful.
sshd is most useful in a laptop where you need capacity, but have room for only one drive.
For performance, put windows on a ssd.
Samsung evo of 240gb is sufficient.
Samsung has a nice free windows C drive mover