Hello Kartiks, thank you for your answer.
I tried with search plugins, ajax product search didn’t work and had to delete the plugin from my host panel because it wouldn’t let me access to WP.
Other plugins get installed as widgets, so if I add them into my theme they go into different areas, such as page footers or on top of the logo.
Checked the code solution, but it seems my theme is overriding the old search.php, so I didn’t find how to work around it.
About the rest, checked around the whole WP admin panel but I couldn’t find anything that would let me change these words, tried to find it in the code but no luck either.
Thank you again for your answer.