The only time you need to add own delays is if you run with a high baudrate, and the receiving side isn't fast enough to extract and process the data as fast as the baudrate allows.
so far so (almost) good, BUT I have seen 9600 receivers that could not keep up so "if you run with a high baudrate" is superfluous


If the receiving side doesn't have a FIFO, then it will not be enough that the average speed of the receiver is good enough.
FIFO not required many apps keep up without one

It must always manage to pick up the next character within one full character time, or the UART will get an overrun error - fully receiving a new character before the previous character was read out.
correct

In some situations, delays may also be used for framing, i.e. a long delay between two characters are used to indicate the start of a new message, while multiple characters received with a very short gap (relative to the baudrate) will be considered part of the same message.
example J1708

Erik