va-diim: Because "być" is not predicative, as "Jakie" is not subject of the sentence. Not everything that comes after "być" goes to instrumental; only predicatives do. E.g.: Jestem tutaj (I am here). Być tutaj. Być wesoły = to be happy, Być w domu = to be at home, etc.

maybe "możliwość" ,

opcja http://sjp.pwn.pl/szukaj/opcja.html możliwość http://sjp.pwn.pl/szukaj/możliwość.html

Możność is rarely used word, meaning circumstances allowing something to happen/ be acomplished

A small addendum: możność , możliwość i możność

P.S. you use some interesting words :)

Jakimi is a totally different thing. It would be clearly question about the properties of something, but posing such a question correctly is not evident, often unnatural and sometimes is quite difficult. It is not a typical question, it may be posed while asking about someone's preferences. eg.

• Jakimi dziewczętami się interesujesz? [What (sort of) girls are you interested in?]
• Jakimi samochodami lubisz jeździć? [What (type of) cars do you like to drive?]

or in singular:

• Jakim on jest mężem? - [What (kind of) husband is he?]
• Jaką mnie wolisz? [What do you prefer me like?] - (clearly a woman asking her closely related man, and it may concern eg. the colour of hair dye, dress, attitude and a whole range of other things including intime behaviour) - therefore it is often necessary to narrow the question down, eg. Jaką mnie wolisz, w rudym czy blond? [What do you prefer me like, in red or in blonde? (showing off with her hair dyed)]

No. It is something different.