it's not question about image optimization, it's about size of image and format. It must be webp
2. I already wrote you reasons.
3. You can't expect good speed on slow hosting
4. Your cache plugin (Autoptimize) is not proper configured and in current point it's slowing down site and breaks all scripts.
We provide paid service for optimization. Price is $120. Includes page optimization and cache configuration. This also can require hosting migration. Depending on budget, we recommend few: WPX (average speed, good price), Cloudways (very scalable and a lot of plans), Rocket.net (high price, but good server response time)