I need to create custom search web part with 3 filters. First filter will have all list names in a dropdown box. Second filter will have particular list column values(only 2 values like active and inactive) in a drop down box. Third filter will have some numeric values that is list column id in text box. Now on clicking search button i need to send query string to search result page with all these values..is this possible? Also i need to know wheather my search page can have multiple display groups for these drop down and any possiblity to add text box filter to existing search options.
I think you should go for CAML query or out-of-box filters instead of search to find items in specific lists.
If you want to use search anyhow, You can create a scope for each list and create managed property for each column to search for. Then, you can see below how to form keyword query with the properties and scopes :
Perhaps not an exact answer but an excellent blog post which will point you in the right direction: http://consultingblogs.emc.com/mattlally/archive/2011/12/29/sharepoint-2010-custom-advanced-search-for-power-users.aspx. At least this should help when it comes to building up the search query.
As for your last questions they will have to remain unanswered by me.
How would the text box be used? To filter the result set? Or, in essence, changing the query string? That should be possible of course.