(1) Upon application, the commissioner may grant to a savings bank full trust powers, as provided in this section, but subject to the conditions, limitations, and restrictions in this section and section 422 to 428.

  (2) Upon approval of the application, the savings bank has the power to conduct a trust business including, but not limited to, any of the following:

  (a) In and by its corporate name to take, receive, hold, repay, reconvey, and dispose of any effects and property, both real and personal, that may be granted, committed, transferred, or conveyed to it with its consent, upon any terms or upon any trust at any time, by any person, including minors, bodies corporate, or by any court, including the federal courts, in the state, and to administer, fulfill, and discharge the duties of the trust for the remuneration as agreed upon.

  (b) To act generally as agent for the transaction of business, the management of estates, the collection of rents, interest, dividends, and money, and the collection of principal and interest on mortgages, bonds, notes, and securities for money and to enforce the payment thereof, and to act as agent for the purpose of issuing, negotiating, registering, transferring, or countersigning the certificates of stock, bonds, or other obligations of any corporation, association, or municipality and to manage any sinking fund on the terms as agreed upon.

  (c) To accept and to execute the offices of personal representative, trustee, receiver, conservator, liquidating agent, assignee, or guardian of any minor, incompetent person, legally incapacitated person, or person subject to guardianship, subject to the laws of this state applicable to those proceedings. In all cases when application is made to any court in this state for the appointment of any trustee, receiver, personal representative, conservator, or guardian of any minor, incompetent person, legally incapacitated person, or other person subject to conservatorship or guardianship, the court may appoint the savings bank, with its consent, to hold the office. The accounts of the savings bank as trustee, receiver, conservator, liquidating agent, assignee, personal representative, or guardian shall be regularly settled and adjusted by the proper office or tribunals. All proper, legal, usual, and customary charges, costs, and expenses shall be allowed to the savings bank for the care and management of the estate so committed to it. In case of appointment by any court, the savings bank shall not be required to give any security except in the discretion of the court, other than as provided in section 426 for deposit with the state treasurer. If the court orders the savings bank to give security, the security shall be a bond in an amount fixed by the court and with a surety company authorized to do business in this state as surety on the bond, or with personal surety or sureties on the bond satisfactory to the court. If any savings bank is required, in the course of the administration of any trust, to give a bond, whether as additional security, substituted security, or otherwise, the surety on the bond shall not be liable directly or indirectly for any act or default committed by the savings bank prior to the date of the filing and approval of the bond, or for the failure of the savings bank to pay over on final settlement if the failure to pay over is due to an act or default committed prior to the filing and approval of the bond, or for the failure of the savings bank to collect from itself or from any prior surety or sureties the amount of any loss due any act or default committed by the savings bank prior to the date of the filing and approval of the bond.

  (d) To exercise by its board of directors or authorized officers or agents all incidental powers as are necessary to carry on a trust business.