Universal remote will be difficult for PIC12F675 with only 64 bytes RAM, but just possible, maybe.
.. and yes, Received IR signal will be different from the the original transmitted signal, as the receiver chip tends to stretch MARK pulses and shrink SPACEs.
The further away the transmitter is from the receiver, the more the distortion, which is why commercial "universal" remotes require the training remote to be located very close to the receiver when learning.
Exact figures are hard to predict, as there are so many variables. I hope you have a Digital Storage Oscilloscope (or better still, Logic Analyser) available, otherwise working out how to adjust the received timing to re-produce close to original transmit timing will be very difficult.
You might want to try subtracting 40uS from each mark value then adding 40uS to each space value, but this is pure guesswork on my part. Use an Oscilloscope to compare original remote timings with your transmit timings to be sure that you have faithfully reproduced the original signal.