1. are we filing the forms properly
From how you have described it, yes that sounds correct to me.
2. if we say we materially participate and are general partners (so that we can deduct net rental loss against earned income on our individual returns), are we at any risk of owing self employment tax ?
No. Rental income isn't subject to self-employment tax even if you materially participate, and/or it's a short-term rental. It would be only if you provide "substantial services", which means services *during* guests' stays, such as daily cleanings during their stay like a hotel (not just between guests), entertainment, or meals. But that's rare and wouldn't apply in your case. If you're putting the rental income on form 8825 (the partnership equivalent of Schedule E), then it is considered just rental income and it won't be subject to self-employment tax.
Q: for any year that is a net loss on the Airbnb, can we deduct that against our earned income on our individual returns ?
Regarding this question, usually the K-1 rental loss from your partnership won't be able to offset your earned income. An exception is if you qualify for the "short-term rental loophole" as it's called. For that, first the average stay for the year must be 7 days or less. And then second, you and/or your spouse must have logged enough hours to qualify for material participation. That means you must spend at least 100 hours/year on it if no one spends more time on it than you (otherwise the requirement is that they spend at least 500 hours/year on it). That is a lot of hours, and if they have a property manager they usually won't have enough hours to qualify, and it doesn't sound like you do in this situation.
