Question: Trading in Options . . .

Is it allowed to buy and sell equity or index options in the stock market?

These options can be 'call' options or 'put' options.

See explanations regarding options on these sites:

http://www.cboe.com/LearnCenter/Faq.asp#options

http://biz.yahoo.com/opt/education.html

http://optionetics.com/education/trading.asp

Is it permissible to 'write' (i.e. create and sell) options, both call and put? These can be either ‘naked' writing or 'covered' writing where, for example, a call option is 'written' (i.e. created and sold) against an existing stock position.

Are more advanced strategies combining these allowed, such as credit spreads, debit spreads, butterflies, and condors?

According to Islamic law, trading in rights is permissible and therefore trading in options is allowed, not to mention trading in equity in the stock market.

Since trading in options is permissible, then concepts like 'call' and 'put' options are allowed too, as well as 'writing' the options; whether 'naked' or 'covered'. 

On the basis of the definitions given in the links you had cited, more advanced strategies such 'credit spreads', 'debit spreads', 'butterflies', and 'condors' are also allowed.

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