Also question is, can you be tracked on incognito?
Incognito does not mean invisible. Google makes it clear that just because you are browsing on Incognito mode that does not mean you are not being tracked. Just in case you didn't know and were blissfully unaware - when you are browsing on the Incognito mode on Google Chrome, you are still being tracked.
Also, does incognito save history on iPhone? The main point of browsing in incognito mode is to avoid saving any history or any data from the websites you visit. Having a backup of the data on your device even in incognito mode can help you recover the data by simply restoring the backup.
In this manner, is Incognito safe on iPhone?
iOS users on Safari can simply select the tabs icon at the bottom right then tap private. With the ostensibly confidential mode engaged, your browser won't record any temporary data on the device you're using. This means that none of the pages you visit will display in your search history after you close the window.
Can the WiFi owner see what I search?
A WiFi owner can see what websites you visit while using WiFi as well as the things that you search on the Internet. When deployed, such a router will track your browsing activities and log your search history so that a WiFi owner could easily check what websites you were visiting on a wireless connection.