You can connect the new drive to that USB to SATA adapter and run that software to clone the used space on your existing drive - pretty fast and very effective. I use this when replacing existing drives with solid states all the time and have very good success with the cloned image without needing to expand the partition
Recently i bought a 1TB SSHD to be used in my laptop. The problem is, that my laptop contains a genuine retail windows 8.1
If i replaced my HDD with the SSHD and install the windows there along with it's product key, will microsoft makes it genuine?
Shouldn't present an issue, worst-case you can always use the automated microsoft line to transfer it if any issues arise.
As an FYI, to avoid any issues, you could always use the Advanced Tokens Manager which will backup the activation, and run the program once you're up and running on the SSHD. I've used it recently & runs perfectly.