Is there an official stroke order for each character?
There isn't an official stroke order for each character, but only a subset of all characters used, and official stroke order exists solely for the purpose of educating schoolchildren.

Japanese stroke order is actually not as fixed as Chinese, and the only reason it feels that Japanese stroke order is more fixed is because Japanese textbooks or dictionaries include stroke order guidelines.


In Japan, dictionary making is actually a competitive business and dictionary content is not regulated by the government. The current reality in Japan can be summarised by the following MEXT quote:


  漢字の筆順は、原則として一般に通用している常識的なものによっており、行書で筆順が異なる字については、適切な説明を加えていること
  
  -- 義務教育諸学校教科用図書検定基準


That is, Japan no longer prescribes official stroke orders for kanji, and lets textbook or dictionary editors decide for themselves, only recommending that they use something that's widely recognised by society. Official stroke order in Japan was actually only in existence from 1958 to 1977 for the Kyōiku_kanji.
Chinese stroke order is less centralised, because there are multiple language standardisation bodies for the Chinese language; the PRC, Taiwan, and Hong Kong independently decide the characters taught to schoolchildren and their corresponding stroke orders. Their official stroke orders don't come packaged with dictionaries given that


Common use characters in Chinese double that in Japan.
The purpose of stroke order is only as a guideline to write characters, not a set of rules.





To address your points,


The following are the official stroke order resources for Chinese language education:


ROC (Taiwan)
Hong Kong
PRC (Mainland China)

There's something called the traditional stroke order, for which all Chinese stroke orders and Japanese stroke orders have diverged slightly from. Traditional stroke order was largely decided based on analysis of the pieces of famous calligraphers, noting that Chinese calligraphy is written from top to bottom, right to left. Chinese standards, at the turn of the century, decided to change some of the stroke orders to make horizontal writing with a pen easier. Japan went another route and tried to optimise stroke order for semi-cursive script.
左 and 右 having different stroke orders are based on their differentiation in  seal script and earlier:



They were originally pictures of left and right hands, respectively, and the first stroke draws the span of the hand while the second stroke draws the arm. Writing both with the same stroke order tends to encourage mistakes in character proportions, and I personally wouldn't recommend it even though some Chinese standard prescribes this.



Notice that the relative length of the slanting and horizontal strokes are different between 左 and 右, a legacy of each of the strokes representing different parts of the hand in 左 compared to 右; using the same stroke order for both encourages sloppy writing.



In rapid or cursive writing, the only way you can tell which one is 左 or 右 is because of their different stroke orders. You're either going to be limiting your own writing speed, or getting in alot of trouble if you get into the habit of speed-writing them the same way...


Finally, you should remember that stroke order is not an end-goal unto itself, but rather something that makes cursive script more recognisable. If you do not plan on writing kanji in the way a fluent person writes in cursive, but stick to regular script instead, then stroke order is not as important to get the message across. However, if you wish to achieve writing speed and fluency, there is a narrow range of acceptable stroke orders which should come naturally to you in time, noting that cursive script often takes shortcuts by joining or omitting strokes so that it is very difficult to actually prescribe a solid stroke order for every character (because different people will take different shortcuts).