I understand some of the Fast Speed Serial options in the Microchip IC cannot be tried in the Arduino Due (such as USBOTG?)?. What I actually need is some Serial Speed close to 2Mbps and a USB Programming Port.
What would make you think that? The chip is the chip regardless of what board it's soldered to. You have the native USB and you have all the UART connections direct to the chip. The board has no effect on that at all. 2Mbps is nothing. You can go much faster than that.
Which are the main differences between the Microchip ATSAM3X8E and the Atmel ATSAM3X8E?
The label. When Microchip bought Atmel a few years back they bought everything. That includes the Malaysian factories where the Atmel chips are made (a friend of mine had the job of inventory combining and spent quite some time in Malaysia sorting it all out). Microchip ATSAM3X8E chips are made in the same factory by the same people to the same designs on the same machines. It's just they are now labelled "Microchip" instead of "Atmel".
I notice there are some functionalities in the Microchip ATSAM3X8E or even in the Atmel ATSAM3X8E not able to be reproduced in the Arduino Due Board?
Is that a question or a statement. Or aren't you sure? The Due is just a chip on a board with some support circuitry. Everything that is in the chip is there, you can't remove it. There may be the case that a specific pin may not be brought out to a header, but you will have to compare the datasheet with the schematic in that case. The chip is not at fault here.
Do The Microchip ATSAM3X8E IC have its own functionalities not present in the Atmel ATSAM3X8E?
No. The two are 100% identical.
As note, there is a Keil ARM SAM3X-EK Evaluation Kit (also also here with its brochure), with a ATSAM3X8H, which is not the same IC series, but somehow exposes my concern (if real).
The ATSAMA3X8H is not commercially available. It was a specific custom chip made only for the SAM3X-EK kit. It is, essentially, a SAM3X8E with more IO pins and the ability to connect to SDRAM.
If my concern about High Speed Serial is real, how should I evaluate it?
Your concern is not real. Only imagined. The only possibility is that the UART to USB chip used on the Due may not be able to keep up at high baud rates. That has nothing to do with what the SAM3X8E can do, just what the interface to your PC is capable of. You can replace that with an external USB to UART interface if you want, such as an FT232R based interface. That is if it's communication with your PC that you're concerned about, in which case you would be better with the native USB interface as it's not restricted by whatever external hardware is added.