Hello,

Regarding your query, the header image you choose for the page from Admin Panel > Appearance > Customize > Header Image will be same for the all pages except the frontpage(as the front page does not have header image). So, you cannot change the header image in individual pages.

Further, for the sidebar, you can use below-given CSS to remove it by following the path Admin Panel > Appearance > Customize > Additional CSS,

.search-results .widget-area{
    display: none;
}
.search-results .content-area{
    width: 100% !important;
}

Hope this helps.

If you have further queries, let us know.

Regards.