Purpose of using per unit when calculating faults?
Good ol' Wikipedia to the rescue. The Per-unit system article states:

In the power systems analysis field of electrical engineering, a per-unit system is the expression of system quantities as fractions of a defined base unit quantity. Calculations are simplified because quantities expressed as per-unit do not change when they are referred from one side of a transformer to the other. This can be a pronounced advantage in power system analysis where large numbers of transformers may be encountered. Moreover, similar types of apparatus will have the impedances lying within a narrow numerical range when expressed as a per-unit fraction of the equipment rating, even if the unit size varies widely. Conversion of per-unit quantities to volts, ohms, or amperes requires a knowledge of the base that the per-unit quantities were referenced to. The per-unit system is used in power flow, short circuit evaluation, motor starting studies etc.
The main idea of a per unit system is to absorb large differences in absolute values into base relationships. Thus, representations of elements in the system with per unit values become more uniform.
[Emphasis mine.]

So back to your questions:

Why convert into per unit? Why not just use resistances ect to calaculte fault values?

While the resistance may help solve a calculation at one particular voltage level - on a 10 kV feed, for example - you then need to scale it to see its effect on the other side of the transformer feeding it - on a 38 kV feed, for example. This gets tedious and confusing. The per-unit system solves this. A per unit measurement on one side of the transformer is the same on the other.
Disclaimer: I don't work in this end of the business and never heard of per-unit measures until it came up in previous questions on EE.SE.