For your home page (startup page), you can change it in the Options. These article have the details:

• Startup, home page, tabs, and download settings
• How to set the home page

To prevent it from being switched back, please check on the following:

(1) user.js file

This article describes how to track down and remove the user.js file that overrides your own settings every time you exit and restart Firefox. How to fix preferences that won't save

(2) Suspicious Extensions

You may have one or more unwanted extensions. Try disabling ALL nonessential or unrecognized extensions on the Add-ons page. Either:

• Ctrl+Shift+a
• orange Firefox button (or Tools menu) > Add-ons

In the left column, click Extensions. Then, if in doubt, disable.

Usually a link will appear above at least one disabled extension to restart Firefox. You can complete your work on the tab and click one of the links as the last step.

Does that help?

to change the home page go to "about:config" change this option "browser.startup.homepage" to "about:home"

to delete the search engine at the search bar click on search icon, click on Organize Searchs, select the search engine e click on delete.