Brown leaf tips on houseplants is often a sign of watering irregularity. Or possibly salts in both the tap water and/or any fertilizers that may have been used. Whichever cause, they are not critical.

Depending on where you are located, this hydrangea should transition into the garden quite easily. But you will need to do so gradually, letting it acclimate to outdoor conditions over a period of time, usually a couple of weeks. And it will not be very happy in full sun. Morning sun and afternoon shade is ideal or filtered/partial all day shade.