How to resign properly as CEO of a small business?

1) You are right: you need to move the money in the work accounts from your personal account to a company account, then close the personal (under your own name) work accounts. If the company is already an LLC or corporation, simply set up LLC or corporate accounts (as CEO, you have the authority to do this). If it's not an LLC or corporation, then unless someone else will take over having the accounts for you--and they'd have to do this voluntarily--your best bet may be to set up an LLC or corporation for it, then set-up the accounts and move the money.
2) There is no way to ensure no future liability for past acts: if you did something during your tenure as CEO for which you could be sued, you could be sued later (e.g. if the problem or issue, etc. has not been discovered yet) even if you resign. You are liable for what you have done.
3) Going forward, you will want to completely disentangle yourself from the company: move the accounts, as discussed above; return all company property; and make clear to everyone you deal with, both internally and externally (e.g. customers and vendors) that you are no longer CEO effective as of a certain date. You want to notify everyone in writing, ideally by some way that you can prove delivery (e.g. email), so that no one has grounds to claim that they though you were still on board and were still responsible for something.