Design woocomerce - full stack development

1. Change existing theme with woodmart. There is a purchase permit. You may need a customs code for layout etc
2. Custom search filter like the following website https://www.expus.gr/
3. Speed ​​improvement
4. The design should look very professional on all pages of the website, not just the home page
5. Creation of xml communication from supplier (I attach file) automatic synchronization of products. With my supplier, everything automatically updates prices and photos.
6. Improvement of appearance on mobile to look very correct.
7. Creating a new pop up newlester
8. Improvement of product pages as well as all pages of the website
9. Shop language Greek

Warning ⚠️ No pointless offers, the maximum budget is the one I write only...

My store is https://gurutec.gr

Some reference sites from Greece that I like
https://www.plaisio.gr
https://www.public.gr
https://www.you.gr/