When writing a put option does your account have to be funded so that if the buyer exercises the right to sell you can meet your obligation, or can you write the put option without the funds to meet the potential obligation?
There is no standard answer to this question. It will depend entirely on what kind of options activities your broker offers and what your broker has approved your specific account for. Consider:
Here's one example of one broker's option trading levels and margin requirements. Of course, your broker will vary, so call your broker for a specific answer.
No, margin rules for options are the most strict of all marketable securities. Of course, I'm all but sure that once marketable credit default swaps get going full steam, options'll be outshined.
Option margin is governed by Regulation T, but exchanges, brokers, etc can apply stricter rules. Here's a short list with the complete CBOE margin manual: http://www.themargininvestor.com/option-strategies---reg-t-margin.html
Per the specifics of your question, if you write a naked put, you must maintain 100% of the value of the put in the market + 15% of the broad index's value or 20% of the narrow index's/single stock's value.
Your put isn't considered naked if you have 100% of the exercise price in cash, 1 short underlying for every put (remember that options trade in round lots of 100 so 100 shares for each security since each security options 100 underlyings), or a put with the same underlying at a higher exercise price dated >= the shorted put.