Yes. Copy the Current Contacts view and add the following to the existing criteria:

AND Display_Name LIKE N'%''%' OR Last_Name LIKE N'%''%' OR First_Name LIKE N'%''%'

The N before the single-quotes designates it as Unicode. The odd character is between wildcards (%) to identify all instances.

Yes, you can filter a view based on audit log entries, including fields edited and dates. See the Contact Changes Past 7 Days view example. Here is an example for marital status changes in the past 30 days:

EXISTS (SELECT 1
	FROM dp_Audit_Detail AD 
		INNER JOIN dp_Audit_Log AL ON AD.Audit_Item_ID = AL.Audit_Item_ID
	WHERE AL.Audit_Description IN ('Updated','Mass Updated')
		AND AL.Table_Name = 'Contacts'
		AND AD.Field_Name = 'Marital_Status_ID'
		AND AL.Record_ID = Contacts.Contact_ID
		AND AL.Date_Time > GETDATE()-30 )

Yes. The simplest approach is to use DATENAME(dw,[Date_Field]) to return the name of the weekday. For example, events that start on Sunday: DATENAME(dw,[Event_Start_Date])='Sunday'.

First, it's important to make sure you're creating the view on the correct page, as there are specific items in the data tree based on which page you're on. If you are on the correct page, has a filtered page been created based off the page you're working on? You want to make sure that your filtered page has a filter clause. When the Platform sees two pages without the filter clause on the same page, it arbitrarily uses one of them to build the data tree in the advanced search. Lastly, ensure you have appropriate permissions to the fields or pages you need.