How to set the YouTube app to play 360p instead of 240p video? In the YouTube app there are only options to play 144p or 240p. Is there any way to make it play 360p?

When I access YouTube from Chrome it plays 360p videos; the quality of the same video was way better when played from the browser.
The YouTube quality settings are determined by each video (although if you select a higher quality, it will default to that for the next time).  Hit the three-dot menu button:



Then the Quality cog button:



Then you can select the quality setting.



Other videos might have more options for the quality setting:



This completely depends on external factors like, for example, the size of the source video that was uploaded to YouTube.

You can also (from the 3-dot menu on the app Home) go to Settings &rarr; General to turn off the "Limit mobile data usage" option, which will allow videos to default to higher quality when you are not on Wi-Fi.