@Bonnie Y.
Congrats on starting your investing. You have chosen a very challenging area. Tax sales are very state specific and the rules vary greatly between jurisdictions.
As to the recoverability of your renovation costs, most jurisdictions allow for some renovation costs in some instances. What is recoverable can be different even in the same state depending on the property, location and use. Generally, recoverable costs have a VERY strict limit to repairs required to maintain the property. For example, repairing a broken or unsafe countertop with similar materials may be ok; replacing a formica countertop with granite probably not.
As to how often the property may be redeemed, many factors affect that; is there mortgage, are the previous owners alive, etc. For tax deed sales ( I assume from your description that is what you are asking about) 10-20% redemptions is our experience.
Pitfalls include improper or incomplete notice of the sale, same for after the sale in some places. Illiquidity, over improving, and scam redemptions may be also concerns until you get clear title.