Is my battery ok?

As long as it charges and works, you are fine. All that data is telling you is that this is not a new battery and will not perform like one. It is a used phone with a used battery with 416 full discharge/charge cycles on it. All battery's capacity declines with age and use. All Lithium cells have a finite useful lifespan and begin to deteriorate from the moment they are assembled.

You can see Apple's tips for optimizing battery life here - https://www.apple.com/batteries/maximizing-performance/

To maximize how long a lithium cell remains useful, try to avoid frequent deep cycle discharges (especially discharging it all the way to the point the device automatically powers off). Deep cycles degrade a lithium battery much faster than shallow cycles, so it is better to actually charge it more frequently to avoid deep cycles. Even if you can only partially charge it, if it is convenient to plug it in for awhile, do so (you will not harm it with partial charge or discharge cycles). You can safely leave it plugged in overnight if you wish to be sure to start each day with a nice, fully charged battery (leaving it plugged will not hurt it, nor will using it while plugged in).

An iPhone battery is designed to retain up to 80% of its capacity for 500 full discharge charge cycles (https://www.apple.com/batteries/service-and-recycling/), so yours is approaching that point. However, if it has avoided a lot of deep cycles, extremes of temperature and not sat static for long periods, many people get longer useful life too. As long as it seems to be working alright for you, then your fine. And, for $79 (USA) Apple will replace it. Apple does not actually replace the battery in the phone you bring/send it. They simply swap yours with a factory refurbished (i.e. like new) unit of the same model and capacity (so be sure to back yours up before sending it in for battery exchange, so you can restore from that backup later).