Hello @gideondavies,
Your issues are replied below:

there seems to be an issue when viewing posts on a mobile that beneath each post (photo) there is a black square (element) showing the category together with the link.

In fact black square (element) showing the category together with the link when viewing post on a mobile beneath each post is not an issue this is feature of the theme. The theme is designed in such way in mobile view.
In desktop there is hover effect so that box appears within the photo when there is mouse hover over that image.But in mobile view there is no hover effect so that box is kept beneath the photo.

can you instead make it so you can click on the photo in mobile view (ie make it responsive) like it is on desktop?

Photo is clickable and responsive as well in moble view.And you can make it like it is on desktop by customizing through child theme.

Best Regards!!!

Hello @gideondavies,
Your issues are replied below:

Just noticed also. I’m assuming there is a way to delete the category menu at the top of page.

Yes there is a way to disable category menu at the top of page.
For this you have to go to Admin Panel -> Appearance -> Customize -> Theme Options -> Header Options.
In this section you will see a check-box saying Show Category Dropdown.You need to uncheck that check-box as shown here http://prntscr.com/a7mvtm to disable category dropdown.

I havent put a menu on yet but will it do the same and can it be positioned centrally below the title on mobile view which is normal? Maybe some more css??

Yes it can be positioned centrally below title with Custom CSS:
First Go to Admin Panel -> Appearance -> Customize -> Theme Options -> Advanced Options.In this section copy and paste below custom CSS in Custom CSS box.

@media (min-width: 481px) and (max-width: 600px) {
#main-nav{
	top: 100%;
    left: 36%;

}
}
@media (max-width: 480px) {
#main-nav{
	top: 165px;
    left: 44%;

}
}

Note:Above CSS will effect in mobile view only.
Hope this will help you.

Best Regards!!!

Hello, @gideondavies

Currently there seems to be problem with site URL that you have provided.The browser shows white blank page.
So we couldn’t provide you with the solution.

Regards!!!