The serial monitor only supports text (ASCII, UTF-8), it cannot print MIDI messages. You'll either have to use a MIDI interface connected to pins 0/1 or software like Hairless.
You cannot use Serial and MIDI at the same time on an Arduino UNO. There's only a single serial port that's used for uploading, the serial monitor and MIDI. You can only use it for one task at a time. Other boards have multiple serial ports.