> Did Britain start out with the same gauge as India?

No. There was some small lines in Scotland using the same gauge as India, but Britain had a bunch of different gauges and eventually standardized on 1435mm ("standard gauge") as that was the most common one.

I don't recall where I read it, but IIRC there was some motivation that they wanted a broader gauge for India because they were afraid cars would topple over during storms. Or something like that.

> Also, what's going on in Australia?

Each territory built its own railway, with no thought about eventually building a cohesive continental network. In some cases narrow gauge was chosen because it was thought to be marginally cheaper than standard gauge.

https://en.wikipedia.org/wiki/Rail_gauge_in_Australia