What exactly is causing these 500 Internal Server errors?

Hi there,
My site https://www.nia.ie/ shows some 500 Internal Server errors both at the front and back end (Admin). My host is telling me that:
"The reason why you are having issues is because the site you have is using too much resource as the errors we can see are: PHP Fatal error: Allowed memory size of 134217728 bytes exhausted. Basically if someone goes to your site, the site is using 1.5GB RAM per user so if you get more then 3 or 4 users your site will crash. My honest opinion is you should get the site code fixed as it should not be doing this."

Furthermore, I did a test, but I don't really understand the results: https://www.webpagetest.org/result/160806_BC_BQA/

I have run some scans with the P3 Profiler plugin which tells me that my theme (I know, Avada is slow) and a few plugins are causing slow load times, but I don't know the best course of action to take. I need all the plugins I have installed (especially the slow ones, Woocommerce and SUMO) and changing the theme is not an option at the moment. Is it just a case of changing hosting providers or is my host right in that there is a problem with my code?

I'd really appreciate some help in diagnosing the problem please.

Thanks in advance,