TL;DR: yes it’s possible without freaking Windows out. Just don’t move the start location/boundary of the main Windows partition or the EFI partition at the start of the disk (end locations are fine to change thus shrinking or growing is fine but moving the whole partition in any direction towards the start or end of disk is dangerous). Be wary that moving the recovery partition typically located after the Windows install partition (often just 100MB but could be twice that and I’ve heard of it up to 1GB in size though usually it’s 400-500MB in size) can break Windows boot recovery but it can be fixed with some commands and breaking boot recovery only becomes a problem when something with Windows seriously breaks though this can happen with something as simple as a failed update on occasion.

Putting Linux after all the Windows partitions should be fine.

Longer answer:

Are you sure F has no use? Usually the Windows OS partition is followed by a recovery partition which includes Windows recovery files as well as on occasion manufacturer specific files and drivers for something like a laptop. This partition normally should be hidden from within windows though can be viewed using disk management tools and diskpart. Admittedly this recovery partition is usually only a few hundred MB. If this partition is removed or simply has its boundaries/start position changed then it can break Windows recovery and result in a demand for an install disk to fix serious errors that prevent boot. For a laptop if you travel with it this could be a minor hassle at some point in future.

Generally you’d want to put Linux after the recovery partition I mention. And if you’re moving the recovery partition you /may/ need to run some commands to get Windows to find it again though then again maybe not. It won’t imminently break things and truthfully if you want to you can generally move the contents of the recovery partition to a folder within the C:/ drive called recovery and use some commands to set that as a location.

I would run reagentc /disable from an administrator elevated command line before moving the location of the recovery partition (this /should/ exist but may not in all cases especially if the machine is older so if there’s no such partition don’t worry). You can later run reagentc /enable after you’ve finished moving it which should restore it to working order.

Windows also has a nasty habit of deleting or overwriting Linux boot-loaders and messing up their start sequence. For this reason it’s strongly recommended where possible (I understand it may not be) to install them on two separate disks. Otherwise be prepared for Windows breaking Linux out of the blue one day, making it unbootable, and requiring you to fix the boot process.

As to your time resetting at start that tends to mean your CMOS battery has died. You can buy a replacement if you want though I’d check out what kind you need. Some laptops you can just buy a standard CR2032 cell and slot it in, others it’s a pain to access (look up youtube videos for your laptop model with the key words “CMOS battery replacement” to see how hard or easy it is and what it looks like). For some models the battery comes welded to some leads in a plastic wrapper, you can sometimes pry the leads off and just electrical tape them onto a new standard battery (do not attempt to weld or solder, the battery will explode, they use a special process to do it at the factory) but it’s usually only a few dollars more to just buy a Chinese model that includes the leads present for a quick and easy swap. Overall I’d expect $2-7 for the cost either way, closer to $2 if it’s just the cell.