I am trying to send real-time data taken from an ADC by Arduino Uno (SPI) to Arduino IDE through a USB cable. I found that one byte takes around 70 microseconds when Serial.write() is used at a baud rate of 115200. My question is that if I send 14400 bytes (which would be the maximum limit at this baud rate), can I perform any other tasks? Does Arduino allow multitasking while the serial buffer is busy writing data?
Until you fill the transmit buffer (64 bytes by default but can be recompiled to enlarge it if you need to), Serial.print() or Serial.write() will return immediately. The characters in the buffer will be transmitted by an interrupt service routine, so essentially, the Arduino is double-tasking for that purpose. If the buffer is full when you call Serial.print() or Serial.write() or Serial.print() fills it before having sent all of its characters, those calls block (won't return) until there is buffer-space for their remaining characters.
So yes, you can do other things while the writing happens, as long as you haven't filled the buffer. You can call Serial.availableForWrite() to find out how many characters you can send without blocking.
By the way, at 115200 baud, or 11520 bytes/second, each character should take 1/11520 seconds or 86.8 microseconds, not 70 milliseconds.