Unfortunately, the Precision T5600 does not have any M.2 slot that can support NVMe SSD.

There is PCIe adapter that will allow you to install the Samsung 990 Pro SSD onto one of the PCIe slot.  That should work but the performance will be limited to the PCIe gen 2 or PCIe gen 3 depending on which slot you will use.  See example of PCIe adapter below.

Using the numbering on motherboard pictured below, these slots can be used for installing the PCIe adapter with your Samsung Pro 990.

Slot 2, PCIe x4 Gen 2 speed.

Slot 3, PCIe x16 Gen 3 speed.

Slot 5, PCIe x16 Gen 3 speed.  May have reserved and occupied by graphics card.

Slot 6, PCIe x4 Gen 3 speed.

Here are examples from shopping site for NVMe to PCIe x4 adapters.  This is the specific item as pictured.

The T5600 does not support NVMe boot natively.  However, one can test with using CLOVER. 

I have written a few posts about the procedure a while back and could not find it.  CLOVER guide can be reviewed from here.

Also, someone has successfully installed CLOVER on T5600.  Info can be reviewed at this discussion.

From personal thought, navtive boot Windows from SATA SSD is only a few seconds slower than boot Windows from NVMe SSD.  You can then installing apps and games on NVMe SSD to improve load times. 

When using CLOVER, it takes several seconds to boot CLOVER USB before it hands over to boot Windows on NVMe SSD.  That combination increased total boot time to become longer than when boot from SATA SSD.

Again, this is just my personal thought.

Am glad that you found all my posts were helpful to your topic.  

As for your question, yes, the storage controller such as HighPoint would work in your T5600 workstation.  Certain HighPoint NVMe RAID controller series are dedicated PCIe direct to CPU and having built-in bifurcation.  Some can manage up to 8 NVMe drives such as SSD7540.

However, those are not a feasible upgrade choice to be used with your T5600.  For storage, you can install two Samsung 990 Pro on separate PCIe slot, just simply use two of the cheap $10 adapters.  They will be visible in your Windows operating system and you can create RAID 0 or RAID 1 using Windows storage space or Disk Management.  They will be excellent performance for Adobe scratch drive or large project that needs high speed and frequent file transfer.  For boot drive, just install one NVMe and create CLOVER USB.  Installing Windows on the NVMe drive and it will boot with the assist of CLOVER.  But, you have to keep the USB always plug in.

You certainly are welcome to ask any questions and thanks for kind words.  I did not have a T5600, however, I have used similar and newer models such as T5810 with the C600 series chipset.  Later, I used T5820 and T7820 (dual CPU).  Therefore, I have gained some knowledge about those workstations.

As I mentioned in previous post, you don't need the Highpoint RAID controllers.  It is not a feasible upgrade and you still can gain the performance that NVMe SSD offered without it.  Your system has Dell PERC H310 host based RAID card supporting SATA/SAS/SSD drives.  You can continue to run operating system from SAS or SATA SSD as you have been.  Just simply add a Samsung 990 pro to the PCIe slot.  O,r adding two separate Samsung pro to two PCIe slots and RAID them if you like (software RAID).  You should get access to very fast storage, up to 3500 MB/s.  Set up in Adobe to use scratch drive located on the newly added storage.  You can also select the Samsung drive as location to install new apps so they can load/launch with the increased speed. 

For BIOS access issue, you can perform an RTC reset and upon restart, you will get a message to adjust system date and time with function keys to access BIOS settings.

If you are still unclear of the reason why I suggest against Highpoint RAID card, it's because of weighing the high cost of expense to gain the benefit of having two Samsung pro on one PCIe slot.

In your case, just spend $20 USD for two PCIe to M.2 adapters.

Only provide you with performance between boot choices I have experienced with.  The setup options and upgrade plan is still yours to make.  In general, the comparison was after second Dell logo (passed POST), it would take up to 15 seconds for SATA SSD to complete boot.  The same after POST, it would take CLOVER 6 - 7 seconds to boot and pass over to NVMe SSD and it would take another 10 to 12 seconds for NVMe SSD to complete boot.

For your BIOS access issue, you already got to the menu but were not able to see the display.  Try to simplify the video connection if using multiple monitor setup.  Check with connection type as BIOS screen has more basic resolution than as of in Windows.  If needed, temporarily test with different video card and/or test with different video ports.

Some users had reported similar issues and were resolved with using some basic Quadro cards to gain BIOS menu display.