Why does HDD activity slow the whole System down (on Windows 7)?

If you're using multiple resources on the same hard drive, then this is normal behaviour. Hard drives are big, mechanical devices which are good at one thing - only doing one thing at a time. You can only read/write to a single sector at a time, so attempts to use the hard drive simultaneously usually result in thrashing. This isn't a side effect of anything other than the hardware working as designed.

If you're doing multiple things on a mechanical hard drive at once, you might find better results by performing these actions one at a time. If you're talking about file transfers, considering replacing the Explorer file copy handler with another program which supports transfer queuing (such as TeraCopy, which will also allow you to pause the transfer if you need fast disk access temporarily).

You can also help to mitigate these effects with the use of a solid-state drive, but it is no guarantee - it only helps because of the drastically reduced random access time. You can still have thrashing with an SSD, and an SSD still has the same limitation - it can only read or write to a single sector at a time.

If an SSD isn't the route you want to go, consider using a RAM disk, performing any data processing in-place in memory, add additional drives (not partitions) for each task, or performing I/O intensive tasks on non-OS drives.

There are ways to copy, that can be throttled.

"FastCopy" can be used to replace the systems copy operations, and it can be set to throttle its own operations. The throttle can be set "globally" or set manually while it is copying. Reverse that :-) allowing fastcopy to go full speed, it can copy way faster, but can choke the system down worse, use a whole core of processor and make high use of ram to do the copy. it allows for either , but I have not tested it in Win7 yet.

"TerraCopy" a popular replacment for the systems copy , allows for pausing of the copy operations. with it you can get something else going, then un-pause to continue. Terracopy is known to be working in win7.

I Have used both the above for copying, but I avoid having it takeover all operations, each of them can have things that it cant do exactally the same as the system. so I make sure that the original system copy is still available somehow.

I had a very similiar problem: Copying a file from HDD via to a slow network (only about MBit/s) share via robocopy. Whole computer was quite unusable. The operating system (Win10) is on a SSD! Even browsing (Firefox is installed to the OS partition C:) was very slow because opening websites generates IO.

Via ProcessHacker https://processhacker.sourceforge.io/ I've reduced IO priority. So the PC stays usuable and copying speed doesn't seem reduced so far.

Are you running anti-virus software with on-access scanning enabled? If so, disable the on-access scan when copying large files around. Put it back on when you're done.

I have seen on-access scan very serious performance problems a few times. It's basically because the disks end up waiting for the AV engine, and that can take a while to scan big files.