Hello,

I saw the screenshots you attached.

1) I have fixed the mobile header and the search bar is displaying. Please clear the cache and check back.

Screenshot for Clarification: https://ibb.co/Lxddxv9

2) Please Go to WoodMart >> Header Builder >> Edit Header >> Mobile header on the right top.

Screenshot for Clarification: https://ibb.co/kXDjQks

Edit the mobile and menu and enable the option to display the categories menu.

3) Sorry but there is no such option available.

4) Please Go to Theme Settings >> Shop >> Sidebar & Page title >> Disable Categories in shop title.

Screenshot for Clarification: https://ibb.co/7G7p3rv

5) Please deactivate all the third-party plugins, activate the parent theme, and check back.

6) Please make sure that the pre-footer is enabled for the homepage by editing the page.

Screenshot for Clarification: https://ibb.co/zs9gbZ0

7) You can edit the links from Woodmart >> Header Builder >> Edit header >> Edit the text HTML element.

And for the categories images please provide some relevant screenshot to check it myself and help you out accordingly.

Best Regards.