Shop Page changes – guidance request

I am creating a shop with Top Store theme. This is a mobile first approach to the e-commerce store.

We wish to implement the following changes to the Shop page:

1. Search in tags as well (Presently search bar searches only product titles, it seems)

2. Remove Title “Archives” and text “home” under it. (Image at Image 1 of shop)

3. Remove Default sorting, latest etc. box / option.

Below points can be seen in image 2 here: Image 2

4. Remove pagination – view all products on the same page (Do we need to install some lazy load plugin for efficient website?)

5. Remove sort box and all products appearing below lower sort box

Kindly advise in terms that a layman like me can understand and implement.

Thanking you in advance.

Regards

The page I need help with: [log in to see the link]