S13 tranny works in an S14. It bolts right up. Just use the S14 5speed speed sensor in it. The S14 Auto speed sensor is physically different (It just doesn’t fit).
You will get the CEL cuz the CPS sensor won’t be plugged in (it goes on the top of the bellhousing and the S13 trannies don’t have that hole on their bellhousing).
As far as I know, the S13 subframe is slightly different. It won’t exactly bolt up the S14 chassis. You’ll have to make it bolt up. Also, any driveshaft from the S13 will be useless on the S14. You must get an S14 driveshaft (ABS or non-abs, make sure you know which one you need).