Is there a legally mandated filing fee and/or deposit in the last instance?

Court of Appeal Rules (CAP. 336)

Section38:

“(1) Save ashereinafter provided, the fees prescribed in Appendix B shall be charged inrespect of the matters to which they are respectively assigned and shall bepaid in stamps.”

Section 27 :

“(1) In any cause ormatter pending before the Court, a single Judge of the Court may uponapplication make orders for

(a)  giving security for costs to be occasioned byany appeal;”

Source: http://eccourts.org/practice_directions/Court-of-Appeal-Rules.pdf