Do I keep copyright when I publish my book through a US publishing company?

[trinitybookpublishers]

Question body:
Hi everyone,

I live in Australia and I am thinking about publishing my book with Trinity Book Publishers, a company based in the Au & US. They offer editing, cover design and distribution, and they say I keep 100% of my rights and royalties.

Before I sign anything, I want to understand a few basic points:

1. Under Australian law, do I automatically own the copyright in my manuscript, or do I need to register it?
2. If a publisher like Trinity Book Publishers edits my text and designs the cover, who owns those edits and the cover artwork unless the contract says otherwise?
3. If the contract is with a US company, which country’s law usually applies if there is a dispute?
4. Are there any clauses I should watch for, such as exclusive rights, termination or fees for getting my rights back?

Has anyone dealt with a US publishing company before, or can a lawyer point me in the right direction? Any advice would be appreciated.

Thank you!