The nature of our present time is very different from Buddha's time: after the printing press "politics" really started taking on an industrial and corporate mission.
On the other hand, the ruling monastic order, the Vinaya in particular was passed on entirely orally. This should answer your first question. Any question on how Buddha handled X, can be answered in the Vinaya.
In my opinion, it is frequently contextual and oftentimes impractical for our times.
We live a different day today: a day of bodhisattvas and renaissance men.
As for specific cases of "politics" which didn't really exist on such an organized level for lack of printing press, there is the case of Devadatta taking over the initial political expression of Buddhism. (Osamu Tezuka's Buddha manga beautifully renders this story.)
Eventually Devadatta tried to kill Buddha, too, symbolizing the message from Buddhism about poltiics: "power corrupts."
Even more broadly, contrived action corrupts, especially socially contrived action tends to create backlashes within and without. We are one collective organism and when good is born, evil persistently tries to take over, day and night.
When there is no contrived good, there is no contrived evil.
This is why Buddhism and Taoism philosophy are often very close, with Taoism taking an even more non-interfering attitude towards things, having the overall expression of "let all karma go up and down, when everyone tires of controlling and contriving, they will rest within the natural order."
The Buddha himself didn't do much in terms of managing the Sangha, just like any of the Zen masters (who are even more strict, some forbidding writing or taking notes). Even when he passed on leadership to Mahakashyapa, all he did was raise a flower and smile (likely paranormal methods of transference involved).
How is politics active in Buddhism today?
Highly active! There is SGI international, Tibetan Buddhism affecting politics in China, and with the marriage of Buddhism and scientific brain analyses, an overall recognition of the importance of samatha and vipassana meditation for happiness and maturity.
I think we have reached an excellent point today and there are many different "politics" with simple rules in smaller meditation circles to clear echelons of managerial staff, teachers, web developers, etc. for mini Buddhist societies. It certainly doesn't seem like the Buddhadharma (whether in the form of Buddhism or other traditions which focus on Insight Meditation) is nearing any sort of Dharma Extinction Age (where it is said that people will be reading and studying but few will have any Realization).