4 SATA and 2 NVME drives in Optiplex 7000 tower possible?

Two m.2 nvme ssd yes.

4 sata drive, probably not good.  It has 4 sata ports but the white one is designed for dvd, and is typically low speed sata 1.  Also the Dell proprietary sata power cable may have three regular sata power connectors (the cable is connected to motherboard 8 pin proprietary sata power socket).  I would say 3 sata is natively supported.  There is one 2.5” bay and one 3.5” bay. You can install two 2.5” drive in the 3.5” bay.

The default power connector for dvd is slim sata not c/w 2.5/3.5” drive.  But if you really want to add a 4th sata drive and do not care about slow speed, you can replace the slim dvd drive with a dvd caddy to 2.5” adapter.  

I don't have a DVD drive in mine, just one 3.5" hdd and I've added 2 m.2 NVME SSDs to it.. I have 4 SATA SSDs lying around so wanted to check if I can add them (after removing the 3.5" drive)..

Where to put it is not an issue; I can just put some duct tape and stick them.. Main question is if the mobo supports 4 SATA drives in addition to the 2 M.2 NVME ones.. There are 4 SATA ports on them mobo. The user manual does not show this combination so was wondering if its still poossible.

Yes mobo will support 4 sata drives as long as you find a power cable that has 4 sata connectors or use the dvd caddy adapter.

bios shows sata 0-3

White SATA ports may be SATA II, not as slow as SATA I.

As I was reconfiguring my 7010 many months ago, for a time boot drives were plugged into the white ports.  But to make sure everything is correct and to make sure I get the max out of it, boot drives are plugged into blue and black ports.  Once doing the switch, I couldn't tell the difference.

I wouldn't be able to find it now, could've been in this forum or this forum lead to the documentation, but the white SATA ports should be at least SATA II.  For all we know they might all be SATA III by now, but then I don't know why Dell would use different colors.

Yes, you can, there's no hardware limitations to prevent you from doing so.
Q670 chipsets supports up to 8x SATA 6.0 Gb/s ports (MB simply not implements all of those).
https://www.intel.co.uk/content/www/uk/en/products/sku/218827/intel-q670-chipset/specifications.html
Even better - MB has 3x NVMe slots (one is NVMe Gen5 CPU-bound).
Since all the data passes CPU (except for "Direct Storage" NVidia technology) - the problem might come from DMI 4.0 bridge bottleneck which for Q670 chipset is 16GB/s (shared between all interfaces, LAN/WiFi, USB, Storage, Keyboard/Mouse,  GPU in wrong {non-cpu bound} slot, etc.) - or 8x lanes by 2 GB/s (in reality around 15 GB/s max due to some command overheads).
Simultaneous use of two NVMe Gen4 drives (theoretically up to 8 GB/s each, in practice around 6 GB/s) attached to chipset can peak at 14+ GB/s, each SATA3 lane can peak to 0.75 Gb/s (4x best SATA3 SSDs - that's 3 GB/s)

Therefore it's nearly impossible to simultaneously use 2x NVMe Gen4 PCH-bound drives and 4x SATA3 SSDs at full potential.

I don't get it why there are several references to problems with SATA power - market is full of SATA Power splitter cables 1-to-2, 1-to-3 (I have one of those costing below £3 on e-bay) and even 1-to-4

SSD consumes much less power than 3.5'' HDD (3x times less), therefore it has sufficient capacity to feed 4 drives.

Agreeing with @sam55todd, SSD's are only 5v vs. 12v for HDD's.