This is a issue of your Hosting/Server. Your Sites PHP Memory is 84MB only which is very low. You should increase the Memory more than 250MB. The Latest WordPress Versions may take more resources. If you read This Article You will find this there
A few of NewsPress users face a problem for 500 Internal Server Error. But, This is Not a Theme Issue. We understand that this is raised from the low resource of your host/server. The features of NewsPress requires more server resources like 250MB PHP Memory, 120sec Execution time etc. You may ask your host to increase these values. You can deactivate the Gallery Block from Appearance > NewsPress Options > Gallery to improve the experience with a low resource server/host. You can also use any caching plugin like W3 Total Cache which can improve your site performance dramatically. We have configuration file which can set the settings for W3 Total Cache for NewsPress Extend. You can download This File, Extract and Upload the extracted file from W3 Total Cache Dashboard.