Mmm... seems a little vague and at such a preliminary stage of thought that i’m questioning the seriousness of your proposed endeavour. Hong Kong is regulation mad in many respects, and starting a travel agency is no exception.
That said:
1 & 2) For ANY limited company you will need to get yourself a business account. This makes your #1 question irrelevant. That said, some banks open accounts to non-residents but you need a good reason.
Yes, you must be physically in HK to open an account.
3) Foreigners CAN setup a travel agency. However the procedure for setting up an agency is complicated: i.e. first join a travel association (such as OTOA, HATA, SIPA etc.) - which typically requires you to already know a couple of members who can vouch for you; THEN join the TIC which requires the $500K deposit mentioned by Drunken Master (note: there’s no exam, that’s for tour guides), and THEN you register with the government’s Travel Agents Registry (TAR) who give the official license. (TAR’s purpose is for financial audit and ensuring agencies are fit-for-business, whereas TIC regulate agencies’ behaviour)
Through all of this, check the specific requirements of each association / body, such as for example the requirement to have a physical (non-shared) office.
If you are handling Mainland Chinese clients, or outbound tours, there are additional requirements involving registration of tours and/or tax levy’s for example.
Depending on what you actually want to do... you can also think about whether an agency is even needed or worth registering.
Note that government has plans to imminently replace the regulatory framework, after which the TIC will be replaced with a more authoritative body. For sure, specific requirements will change after this. Something you should keep an eye on.