I have a question about trademark. If my company is based in Australia, and our servers are located in the United States, would we still have 100% trademark right for our company name in the US and also worldwide? Also, which country's law do we have to follow? Like those privacy conditions stuff, etc.
NO, trademarks must be registered in each country. Trademark law is very finicle and must be defined to each country under there local law to protect in the event of arbitration. I have serveral TM in NZ and must do the same for each country I wish to be protected in, in NZ the NZ MED (ministry of economic developemnt) will help me do this but my recomendation is use an IP lawyer as this can be very tricky ground.
Follow a tradmark reg in the US on behalf of a Aus company, again the IP lawyer will get this right for you. They will advise for free give one a call, they will also advise a potential cost.