How is the word 'relevant' different from other adjectives like it?
Some common synonyms of relevant are applicable, apposite, apropos, germane, material, and pertinent. While all these words mean "relating to or bearing upon the matter in hand," relevant implies a traceable, significant, logical connection.
// found material relevant to her case
When could 'material' be used to replace 'relevant'?
The words material and relevant can be used in similar contexts, but material implies so close a relationship that it cannot be dispensed with without serious alteration of the case.
// facts material to the investigation
When can 'apposite' be used instead of 'relevant'?
The meanings of apposite and relevant largely overlap; however, apposite suggests a felicitous relevance.
// add an apposite quotation to the definition
I don't have references for this, but I would be inclined to refer to your unnamed elements as superstrings, because your question is not really about prefixes, but about (prefixed) substrings; and a string that contains substrings can easily and logically be referred to as a superstring. (If you want to be more specific about it, you could call them "containing superstrings", which seems more appropriate in your example 2.)
You would probably do well to use the word elongation.
ban is a prefix substring of banana so banana is an elongation of ban.
The word extension came to mind first, but in computer science, extension refers frequently to a filetype extension following a dot, so that could be confusing when used in a separate context. Elongation carries the same meaning without the risk of confusing readers or listeners.
Per Merriam-Webster definition 2:
a : the state of being elongated or lengthened; also : the process of elongating
b : something that is elongated