Mobility Options From Australia

This is largely a repost with several tweaks to make it relevant to HF.

Context: Currently studying a strong finance course at an Australian university that historically has placed extremely well into investment banking. I tried investment banking over this summer and found that it did not suit me. Was going to aim for ER or HF in my penultimate year, to explore options that tie more into my initial interest of investment. Given that it is Australia, several HFs do offer graduate positions, but often are only Australia-based (would have to rehire to move internationally).

Given that Australia has a small HF industry compared to London/SG/NYC, I want to have that option to move overseas, but would love to build my investment acumen in a HF environment here. 

I was wondering if anyone had any info on:

1. Is transferring internationally as a rehire in HF possible from Australia to SG/London/NYC? My preferences are in that order.
2. Would an Australian grad be able to compete for grad roles in Singapore directly (either HF or ER)?
3. Given that many funds in Australia (Pinnacle affiliates, Platinum, etc.) take grads directly, would it be worth going this route and then transferring overseas? I looking at ER as I thought the more intense environment would be a better training ground as a young professional, and the international brands would allow for international mobility