All filters that BeTheme have are "Category", "Author" and "Tags" - there is no possibility to filter it by date - you would have to edit wp and betheme files to achieve that.
Also, the Search Field can be turned on, but only on menu. (or attached by wordpress widget)
Theme Options > Header & Subheader > Extras, there you will find the "Dropdown" menu with the search option to enable.
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