This may be old advice, but I've always heard never resize down. It can work if you're lucky and there's no data in the space you're shrinking, but if there is data there, it'll often fail.

If the hdd is the same size or bigger than your ssd, I'd recommend cloning the ssd to the hdd. This will wipe your hdd, but should keep windows fine. Then do a clean install of linux on the ssd.

Okay. Let's first start with the obvious : any attempt to change partitions may result in data loss. Before starting, backup everything you can't afford to lose.

Now, the reason it might fail is because Windows tend to enter some kind of hibernation state, rather than truly shutdown.

You first need to disable fast boot. To disable Fast Boot in Windows, press the Windows Key + R, type "powercfg.cpl" and hit Enter. In the Power Options window, click "Choose what the power buttons do," then uncheck "Turn on fast startup" under Shutdown settings. If that doesn't work, follow any instruction online to disable it.

Now, when shutting down Windows, hold the shift button when you click on shutdown. It might take a long time to shutdown, that is to be expected (might take anytime between 1 to 10min). Do not panic, do not force shutdown.

Now you can open Gparted. Please note that data loss is possible when touching the partition table. This is your reminder to backup. Resize your partition and hope for the best.

EDIT : Mind you that moving a Linux partition to another Linux partition is always bound to fail if you don't know how to change GRUB config files (+ maybe other cfg). If you don't know how, or you are unsure, don't attempt it.

Your best course of action would be to reinstall a new Linux distro on the newly created partition, then moving your old files. Don't reuse a home partition if one is already present, it is bound to fail miserably.

If you're unsure which FileSystem to use, go with the default one your installer comes with.

EDIT 2 : Seeing the planned partition table, don't shrink Windows to 300Gb when 275Gb is already used. It might lead to errors and data loss. When resizing, it is best to have a free space corresponding to minimum 10% of your SSD capacity (in this case 50 Gb) to minimise errors.

Either resize to 325Gb or lose some Windows disk space.

Great question. I'm in a similar boat. I set up to dual boot and I haven't been back in months. I guess I'll copy my /home to an external drive and start over half of my data is on 20 year old spinning metal, so I should take the opportunity to get some new drives.