The logo should resize based on the screen size.
You can edit xml/Vertex.xml to add items to the responsive lists, just look for the following code:
<field page="Responsive Layout" version="ge,2.0" name="xml_s5_responsive_tablet_hide" type="multselect" vars="#s5_header_area1,#s5_top_row1_area1,#s5_top_row2_area1,#s5_top_row3_area1,#s5_above_columns_wrap1,#s5_middle_top_wrap,#s5_above_body_wrap,#s5_below_body_wrap,#s5_left_top_wrap,#s5_left_wrap,#s5_left_inset_wrap,#s5_left_bottom_wrap,#s5_right_top_wrap,#s5_right_wrap,#s5_right_inset_wrap,#s5_right_bottom_wrap,#s5_middle_bottom_wrap,#s5_below_columns_wrap1,#s5_bottom_row1_area1,#s5_bottom_row2_area1,#s5_bottom_row3_area1,#s5_footer_area1,#s5_pos_custom_1,#s5_pos_custom_2,#s5_pos_custom_3,#s5_pos_custom_4,#s5_pos_custom_5,#s5_pos_custom_6" default="" label="TPL_FIELD_RESPONSIVETABLET_LABEL" description="TPL_FIELD_RESPONSIVETABLET_DESC" />
<field page="Responsive Layout" version="ge,2.0" name="xml_s5_responsive_mobile_hide" type="multselect" vars="#s5_header_area1,#s5_top_row1_area1,#s5_top_row2_area1,#s5_top_row3_area1,#s5_above_columns_wrap1,#s5_middle_top_wrap,#s5_above_body_wrap,#s5_below_body_wrap,#s5_left_top_wrap,#s5_left_wrap,#s5_left_inset_wrap,#s5_left_bottom_wrap,#s5_right_top_wrap,#s5_right_wrap,#s5_right_inset_wrap,#s5_right_bottom_wrap,#s5_middle_bottom_wrap,#s5_below_columns_wrap1,#s5_bottom_row1_area1,#s5_bottom_row2_area1,#s5_bottom_row3_area1,#s5_footer_area1,#s5_pos_custom_1,#s5_pos_custom_2,#s5_pos_custom_3,#s5_pos_custom_4,#s5_pos_custom_5,#s5_pos_custom_6" default="" label="TPL_FIELD_RESPONSIVEMOBILE_LABEL" description="TPL_FIELD_RESPONSIVEMOBILE_DESC" />
Keep in mind that this is considered custom coding, so there can be no support if any of your changes break anything. Also: The Vertex.xml file is a framework file, so if you install the
Vertex Upgrade Patch, you'll have to re-apply your changes.