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In the PIC16F1938 Timer0 is 8 bit.
In the PIC16F18857 Timer0 is 16 bit.

#fuses is processor specific. You must manually change it to match the new processor.

#use delay can be used to set up the clock input without needing the #fuse directive.

#use delay(clock=4M, ...

With that processor, the CPU can only run at up to 32MHz. The PLL can be used to get 48MHz for the USB.
You cannot run the processor at 64MHz.

Look at the C/ASM list file.

You should never allow your program to reach the end of the main. Add a while(1); before the closing brace of main.

main()
{
printf("Hello World");
printf ...

I don't have that part, but probably use the setup_oscillator function and let it set the fuses.
setup_oscillator(OSC_CLOCK, 20M, 140M);

Guaranteed correct operation of all peripherals will be less than one clock cycle.
YMMV

I am not giving you code, just some direction.

capture a rising edge, save as Rising1
capture a falling edge, save as Falling1
capture a rising edge, save as Rising2

time high = Falling1 - Ris ...

A full cycle has three time readings, not just two.
Rising edge, falling edge, & rising edge
or falling edge, rising edge, & falling edge.

Your code is currently capturing every rising edge of the signal. If you want to measure the time high or time low you will need to capture both the rising edge and the falling edge.
You can either ...

Not in a properly written program.
10ms is a long time from a microprocessors view.
200ms is a short time from a human response view.

To debounce a switch input you would not use an external interrupt or a change interrupt at all. Just poll the pin input at a regular interval and look for a stable change of state.
An interrupt on ...

The contents of the RAM are undefined on power up.

If you want to do int8 x int8 with a 16 bit result there are a few ways.
standard C rules:
100L*foo
(uint16_t)100*foo
CCS function to do 8x8 multiply with 16 bit result (fastest)
_mul(100,foo)

It seems like you would need to use the 8kHz pulse to trigger a one-shot pulse and would go low for 31.25us and then go back high.