10GbE sfp+ cross over cable required? Is there such a thing?

The "crossover" is already built in to these cables. When working with cables like these you don't have a concept of a DTE side and DCE side as you do with ethernet cables. On a typical ethernet cable the DTE(terminal) side will have transmit on pins 1 and 2, with receive on pins 3 and 6. The DCE(switch) side or the other end of that cable will be flipped with transmit on 3 and 6 and receive on 1 and 2. These direct attach cables are built with the transmit of one side built already connected to the receive of the other.

Automatic MDI/MDI-X is required part of Ethernet standard since 1Gbps era.

I'd guess that it is just disabled (either BIOS or driver level) in your case.

There are two types of DAC cables, Active and Passive. You might have the wrong cable for your SPF+ ports.