Remember that internal interrupts are maintained until serviced, external are not unless they are edge, not level

Keeping the sub-routines short means using flags as Pranav suggested
Not necessarily, Many other ways exist e.g. circular buffers.

Keep ISRs Short and SSimple.
Handle the time dependent event e.g. read the UART byte, then get out of there.
The "flag" method sometimes leads to lost data, the "do the time dependent, get out" does not with proper design.

Many "unexplainable" problems I have found came from long ISRs. One one occasion the "flag method" was the culprit. I have never seen a problem with the circular buffer method once it was properly designed.

Erik