Which is the same thing for all intents and purposes.

An ultrafinitist is still allowed to call that 'i'.

You don't. He basically defines numbers like pi and e not as numbers, but as iterative functions, which you can run to whatever level of accuracy that you want. It's sort of a silly argument, because _all_ numbers can be treated like the output of a function, including the real numbers, so he has basically smuggled in all reals through the back door, because any real number can just be thought of as a function with increasingly precise return values with an infinitely long description, just like pi is.

By fiat, of course. :) (e.g. https://en.wikipedia.org/wiki/Indiana_pi_bill)

It depends on the particular construction. You could construct the "complex rational field" by adding i to the rationals with the rule i^2 = -1. That seems to be what Wildberger is ok with. The standard complex numbers involve adding i to the real numbers, which Wildberger doesn't like.

I don't know how you'd do electrical engineering with the rational complex field, because electrical engineering and physics in general involves a lot of irrational quantities and calculus, and the standard foundations of these concepts use real numbers.

It's really up to finitists to show that there are problems with these methods and that they have a better way of doing things, because so far the standard way seems to work very well.