What is the difference between enhanced category 5e cable rated for 400 MHz and category 6 cable rated for 250 MHz?
Category 5e requirements are specified up to 100 MHz. Cables can be tested up to any frequency that is supported by the test equipment, but such measurements are meaningless without the context of applications and cabling standards. The Category 6 standard sets minimum requirements, up to 250 MHz for cables, connecting hardware, patch cords, channels and permanent links, and therefore guarantees reasonable performance that can be utilized by applications.

If we use a Cat 5e RJ45 connector and connect it to a Cat 6 UTP cable, will the installation be Cat 5e or Cat 6?
By definition (of the standard), it will be a Cat 5e channel. The actual performance will probably be somewhat better, but nowhere near Cat 6 requirements. Of course, you can set up a channel using any components and measure it using a Cat 6 (level III) compliant tester, and if it passes, it is Cat 6 performance compliant. It would not be standards compliant however, because the components have requirements in and of themselves to assure interoperability with other Cat 6 components.

Why did Cat 6 cables use to have a spline earlier?
Some Cat 6 cable designs have a spline to increase the separation between pairs and also to maintain the pair geometry. This additional separation improves NEXT performance and allows Category 6 compliance to be achieved. With advances in technology, manufacturers have found other ways of meeting Cat 6 requirements. The bottom line is the internal construction of the cable does not matter, so long as it meets all the transmission and physical requirements of Cat 6. The standard does not dictate any particular method of cable construction.

Is a Cat 6 connector also an RJ45 and will it fit into a Cat 5e socket?
The physical dimensions of the Cat 6 connector interface are identical to Cat 3, Cat 5, and Cat 5e modular connectors and are fully backward compatible.

What will happen if one mixes and matches different manufacturers’ hardware?
If the components are Category 6 compliant, then you will be assured of Category 6 performance. Consult the manufacturer for specific warranty provisions that may be applicable.