I think BP is a UK company and I'm not that familiar with the specifics of their accounting system. In the disclosure they say they considered that they had "significant influence" which is an IFRS accounting term. That would mean (as simply as I can explain it) that the initial purchase is recorded at cost with their share of Rosnefts profits and dividends recorded against that holding (along with a large bundle of other accounting details).
No, they were treated using the equity method:
Depending on what goes on here market wise before they can exit their ownership stake (if they haven’t already!) is what will decide how big a loss this is.
Not quite an SEC rule, just self interest.
You want to get the best price for your stake and your options are to liquidate over the course of a few days in the open market (in which case word gets out) or private placement (usually the best option).
Edit: looking at the BP disclosure, they've decided to make the accounting changes that show they're going to sell the stake, they'll likely be looking for a smart way to offload the shares, probably to some large buyer (not just pressing sell on some brokerage account).
Edit 2: the $25B figure isn't really that accurate. Before this all kicked off, Rosneft had a market cap of around $70B,and BP held about 20%, or $14B. The article sums BP's carrying value for the company ($14B, coincidentally I think), and an accumulated foreign exchange loss of $11B, which had already been charged to equity. The current market cap of Rosneft is about $30B,so the actual hit to BP sharebolders will be something like $8B if they could sell at current prices.