First LP check: where do I actually sit if the deal goes bad?

I was in the same place a year ago coming from the same direction, so taking your questions in order.

The pref is a priority, not a promise. It says the first 8% of distributable cash each year goes to LPs before the sponsor takes profit. If the property doesn't produce cash, nothing is owed to you the way interest is owed on a note. If it's cumulative, the shortfall accrues as a claim to be paid later. If it's non-cumulative, a missed year is gone. Check which word the document uses, because they look identical in a deck.

Sponsor co-investment is usually pari passu with LP common equity, meaning their dollars sit right next to yours and take the same first loss. Read it, though. Some sponsors invest through a separate class with different rights, and a few fund their share with the acquisition fee, which means their cash at risk is smaller than it appears. Ask what percentage of the equity they're putting in and where it came from.

Preferred equity or mezz would show up in the sources and uses table and in the capital stack description. If the sources column shows something between the senior loan and the common equity, that's your answer, and it sits ahead of you in the waterfall.

K-1s arriving in March or later is normal in this world, and extensions are common for LPs in multiple deals. How you handle that on your return is a CPA question. What I'd judge a sponsor on is whether they tell you in January that the K-1 will be late, rather than going silent until you chase them in April.