MIDI Keyboard control
Is there any way to detect MIDI messages that does not require the additional circuit and just uses the USB cable?


You could probably do it with a "USB Host Shield", though I have no experience of them and don't know if they can handle MIDI - you'll have to research this.


  Although in theory control of the LEDs should be easy in the program, I am concerned that the delays in the serial communication and hardware interrupts would make it difficult to simultaneously receive the MIDI messages and control the LEDs.


Highly unlikely. You'd have to be doing something very wrong to make it so slow to respond that you'd see any delay.


  I am not sure, however, if MATLAB is suboptimal compared to the standard Arduino IDE.


I cannot comment, I have never used MATLAB. If you don't use a USB Host Shield then you will certainly require something that runs on a PC to forward the MIDI information over serial.  Whether you create that in MATLAB or some other programming language is neither here nor there as far as the Arduino is concerned - you'll still need to program the Arduino itself, and that can be done in the IDE and still use MATLAB for the PC portion of your setup.