Legal Question in Wills and Trusts in Florida

A trustee can be removed for failing to provide fiducial responsibilities. Depending on what the trust states, it is not unheard of to have different accounts due to the amounts that are covered under federal reserves so one may want to break up the funds in the event a bank goes under.

Unless restricted by the Trust Agreement, yes an irrevocable trust can set up as many accounts as they like, and invest as they like. Normally the Trustee is the signatory. However, they may be able to arrange a discretionary account to a broker. This can be cancelled at any time.

Beyond that, I don't know what you mean exactly by "trustee appoints signature." Though the answers would be in the Trust Agreements Powers Clause, and also pursuant to Florida Statute which may contain additional powers or restrictions.