@SUSANNA-FREYMARK, there is the options to hide date and category inside theme customizer. Please follow the screen record
https://www.awesomescreenshot.com/video/5469067?key=6fddb78e8bad0e5f73b5f91cd695a284

And can you please confirm is that the parts inside the red circle that you want to hide
https://www.awesomescreenshot.com/image/14378869?key=2fd334b780e855879846ce8aebf58edf

If that’s the one, please add this css in the additional css to hide header image

.single-post #page-site-header {
    display: none;
}

hope this will cover to solve your issue

Oh, sorry I thought it’s for a single post page.

here is the new code, to hide the date and category of the posts on the homepage, add this in additional CSS

.home .entry-meta {
    display:none;
}

and this to fixed topbar search design issue

@media screen and (min-width: 1025px){
  .main-navigation form.search-form input {
    padding: 0 10px;
    padding-left: 60px;
  }
}

form.search-form button.search-submit {
    left: 20px;
}

@media screen and (max-width: 1024px){
   .main-navigation form.search-form input {
     padding-left: 60px;
   }
}

Your homepage looks something like this – after adding code in additional CSS
https://www.awesomescreenshot.com/image/14425691?key=71260feaffc284d2193103f98bd9b10f

Please let us know if you have any other issues that needs to be fixed

please add this CSS in the additional CSS

#posts-slider .author-wrapper {
    display: none;
}