Hi Charlotte,
I hope you are well today and thank you for your questions.
1- FORMATTING POST/HOMEPAGE – In the home page of my blog the formatting of the post disappears as you can see in the print attached (1.png). It’s possible to change that and in the homepage appears like it’s in the post page? charlotteontour.com if you want to see what I’m talking about.
You can achieve this by adding the text along with markup in the post excerpt field that you want to display on the home page.
2 – POST FORMATTING – How can I had more formatting options when I’m writing my posts? For example, more text size options. We have available h1, h2, h3, h4, h5 and h6. Can we change those? And can we add more?
You can use the following plugin to achieve this.
3 – SLIDER – The photo that you put to appears in slider can be different from the photo that appears in the post?
You can try achieving this by using pages for the slider using the solution posted in the following topics.
https://colorlibsupport.com/t/using-pages-rather-than-posts-for-flexslider/#post-52391
https://colorlibsupport.com/t/slider-for-pages/#post-33351
4 – SLIDER – I put the code for change the font color on the slider and it works! But the hover part disappears! It’s possible to put the font black and still when you pass the cursor it becomes purple?
You can try achieving this by adding the following CSS code in the Custom CSS option of your theme on the below path.
Admin Area -> Appearance -> Customize -> Activello Options -> Other -> Custom CSS
.flexslider div.flex-caption a, .flex-caption h2 {
color: #000;
}
5 – SLIDER – How can I change the font/text in the slider? It’s possible? Like, text disposition (in the bottom of the slider, in the center, on the right, on the left, etc), text size, font type, etc.
Yes you can change it by developing CSS code.
All the best for your Adventures 
Best Regards,
Movin