What exactly does "capitalized" mean? Does it mean that the home improvement costs are added to the value of the home, and the cost is depreciated over 27.5 years?
Also, does the fact that I own >10% interest in the investment deem me as an "active" participant, and as such: I can offset passive losses against any income? I am not interested in flipping, just holding for rental income.
Yes, it must be depreciated over time. That could be 27.5 years, or less, depending on the scope of renovations, what was done, if there is a possibility to segregate costs, etc.
Your ownership does not mean you are active. I can own 99% of a business, but hand off all the duties to a manager and be passive. Or I can own 20% and be a silent partner, still passive. I can own 1% and do all the work, that would make me active.
There are specific IRS criteria for what makes you active, especially in rental real estate (which is a default passive activity unless you meet the specific criteria).