Multiple Search Forms on website

I have a Woo Commerce website, and the website also has Blogs, Pages, and other contents.

On the Shop Page, I need a Search bar that will search only Products and Product related attributes like Price, SKU, Category,
Tag, Attributes (for custom ones like color or size).

Then on the Resources Page, I need another Search Bar that Searches everything else.

This means that I am looking to have 2 instances of a Search plugin, because I am thinking that I don’t want to install 2 different Search plugins– where one is specifically dedicated to Woo Commerce, and another is dedicated to searching other items except Woo Commerce Products.

Can your plugin be used to create these two instances that I am looking for ? — where there will be 2 different Search Bars on different places of my website, and one instance will search Woo Commerce Product plus its related Attributes, and the other instance will search everything else ?

If Yes, how do I do this ?

2.) If the plugin Ajax Search enabled, to produce result as you Type ?

Regards.