Implementing the custom search

How do I achieve below in Lithium:

I have a custom search box which is being used to search the community, I want it similar to what Lithium is providing by default.

a.) Return the results in a dropdown as we type. [This is been achieved via ajax call in jquery from Custom Component]

b.) On clicking the search, I want the search results to appear on the custom search page, just like lithium's default search page. [Please provide your thoughts on this, how do I submit a form and show the result on a custom search page, custom search page is not yet created]

c.) I would like to add filters, but these can be added only when I take the user to the results page.

d.) The reason I am using the custom search is because we have to club our search results with one external source as well, where in we will serve the results from Community and The external resutls using REST API in the endpoint.

e.) Then we would group the results in tabs, i.e. results from community would be in community tab and external in the other.

At present, I am looking to get through the point b.

Thanks