Firefox is a web browser, Yahoo is a search engine and e-mail provider. It looks to me that you are actually using Internet Explorer as your browser, it is the default browser that comes with Windows.

To answer your question, yes, all your bookmarks and history will migrate. Here are some links to learn more!

How to install Firefox on Windows

Import Bookmarks and other data from Microsoft Edge

Get started with Firefox - An overview of the main features

Just to add on to the previous reply:

Some of your data is stored by Internet Explorer and Windows, such as your Favorites that appear on the Start menu, and the address of your home page.

Some of your data is stored by websites you use, such as your Yahoo! contacts and the contents of your My Yahoo! page.

Firefox will try to copy over your IE settings to get you started, and if something is missed, forum volunteers can explain how to get it.

Also, IE isn't going away -- the blue e will always be there for you in case you need it for something. Please don't try to remove it because some sites like Windows Update are designed only to work in IE.