Items do not mysteriously disappear from your bank, so it seems your account may have been hijacked, as is the case for most people whose items go "missing". The same is true for any items that may be equipped or in the player's inventory. If you suspect you have been hacked, please run a full scan on your computer using Malwarebytes' Anti-Malware and Lavasoft Adaware . When the scans complete, clear your system of any threats detected. Once you have done this, you should be able to login to your RS account to adjust your password.
I would strongly suggest setting up JAG (Jagex Account Guardian) to prevent future unauthorized access to your account. Unfortunately, Jagex does not compensate for players' lost items when someone has been hijacked, so you'll have to work for your money's worth from scratch.
If you broke the rules of the game and received a warning (in the form of temporary or permanent mutes or bans), Jagex may take action against you -- if you used botting software to automatically play the game for you, then they have the power to reset/clean your bank in addition to temporarily/permanently banning you or otherwise adding an infraction or blackmark to your account.
To avoid getting hijacked, do not visit dodgey websites or download software that promises something (for example, party hat or gold generators) as these likely contain keyloggers that will steal your account details and provide the hijacker to login to your account and access your in-game bank. It would also be a good idea to not visit the websites bots advertise in-game and to run scans on your system on a weekly basis to ensure your computer is not infected.
Another popular method hijackers use is phishing -- often in the form of an e-mail sent to you that appears to be from Jagex, or representing RuneScape in any other way. Be suspicious of e-mail that:
If you clicked a link in a phishing e-mail, do not login to the site even if it appears legitimate and scan your computer ASAP. Afterwards, you may want to consider changing your password to be safe.
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While on RuneScape PVP worlds, if you die, you only lose the items you are carrying, not those in your bank, never in RuneScape will a death directly affect your banked items.
No. But if you go into the lose all your items portal than yes.
Nope, you can only place items in your bank using one button.
Only items obtained through quests.