Your logs are mostly 503 errors, which is due to an ongoing issue involving high volumes of traffic against our webmail service. We're working on mitigating that now.
Note that this is different from 502 bad gateway, which is normal when Apache is restarting on the server. That happens approximately every 2 hours and usually lasts 5-10 minutes on Johnny. It's faster on Tommy, and currently doesn't happen at all on Morty due to newer hardware and having so few users and domains on Morty.
Static pages will always be fastest because there's no server side scripting, and will typically not be affected by 503 errors.
InfinityFree's service is faster for a few reasons:
They have a massive for-profit corporate parent company (iFastnet) with huge amounts of money and can afford millions in server costs, so servers aren't crowded. We're a tiny nonprofit with an operating budget of <$10k/year that owns our equipment and has no corporate parent. We can't easily afford more servers.
Infinity Free is artificially crippled. Those restrictions tend to mean people don't stick around for very long, and they can't run larger applications if they do. Our free Johnny service and the one-time-donation Tommy plans aren't. To give you an idea, 96% of our shared hosting users are free users, or are one-time donors who donated as little as $1 for lifetime service.