Electronic – Is using a shorter timer period less accurate than using a longer one

I would use timer 2 to set up a periodic interrupt. 1 ms (1 kHz frequency) is usually a good interrupt period. At 4 MHz clock frequency you have 1 MHz instruction rate, so 1 ms interrupt would be every 1000 instructions. You should be in and out of the interrupt in a few 10s of instructions, so that is a small overall burden on the processor.

To get long delays, set up a counter that the interrupt routine decrements if it is not zero. When this counter reaches 0, the interrupt routine sets a global flag. If you need 1 ms resolution for your 1 s time, then you make this a 16 bit counter. If 5 ms is enough resolution, then you divide the 1 ms tick in the interrupt routine by 5 to make a 5 ms tick, and decrement a single byte counter every 5 ms. If you really only ever need 5 ms timing, then you can set up the periodic interrupt to be 5 ms (every 5000 instruction cycles).

To use the delay, the forground code clears the delay elapsed flag and writes the delay time in units of 5 ms to the counter. The foreground code checks the flag regularly to see if the delay has elapsed. In the mean time, it can perform other processing.

Stop and think about what it means to set timer 0 to FFh. That means it will overflow and set the interrupt condition on the very next clock. The clock is stopped for a couple of cycles when TMR0 is written, so this will occur 3 cycles (if I remember right) after the write. How can you possibly expect the interrupt mechanism to repond that fast. The return from interrupt (RETFIE) takes 2 cycles alone, and the entry into the interrupt routine at least another 2 cycles (it's essentially a call), then there is the code to save and restore context. This is all overhead even if your application code does nothing.

Expecting a PIC 18 to interrupt every 3 cycles is rediculous, as even a cursory look at the datasheet should have made obvious. Using a compiler on top of that only makes the minimum interrupt frequency that can actually be handled worse.

If you want to set up a periodic interrupt, start with timer 2, not timer 0. That timer has a period register for exactly this purpose.

Even if you are stuck with timer 0 to create a periodic interrupt, you should be adding a value into TMR0, not setting it to a fixed value. That way there is no accumulating error and the number of cycles from the timer 0 overflow to the instruction that writes it to a new value doesn't matter.