tldr version: don't worry.

Only slightly longer version: there were some early issues with batteries. These were a good number of years ago now, there have now been nearly 800 delivered, flying every day without issues.

You can see here all the deliveries so far, it's a significant number and if there were still problems, you definitely know about it by now!
https://en.wikipedia.org/wiki/List_o...and_deliveries

You can also read up on the battery problems here, you can see for yourself it's not been a concern for 5 years now.
https://en.wikipedia.org/wiki/Boeing...ttery_problems

And finally, with regards to the engines, yes there have been some issues with the rolls royce engines but they're being addressed over time and those that are flying have been thoroughly checked.

And finally finally, flying from New York, you are actually always fairly close to an airport. 90 mins or so from Iceland or Newfoundland for example.