Website load time and Chrome cache

Hello everybody, I have 2 questions.

1) There is a huge problem with the loading time of my website. When I bought the host packet at X company they told me that I will not get loading problems even if I am in Greece, but guess what I do. The problem with my site is that it takes 5-7 seconds to load a single page, even if the page has 1 photo. The thing is that when it loads, it loads completely. So my question is, any plugin that I can use to load my site part by part so the user will not think that the site is down and leave?

2) Because of the loading problem, I installed W3 Total Cache. I watched a tutorial on YouTube and did all the settings. The problem was with Chrome. I had cached my front page, and everytime that I was visiting the front page on Chrome it would not show the new posts, just the old ones. So, I guess that’s some cache problem. In order to show the newest posts of the front page I should clear my cookies. Thus I disabled the W3 Total Cache from caching the front page. Does anyone know how to fix that on Chrome and enable caching my front page?

* Even with front page cached I had problem with my loading, but a bit less. 3 seconds to load a single page with 1 photo, not bad though.