Hi,
1. Yes, you can change most of the typography here to your custom font: https://i.imgur.com/ZZz9okS.png
If you simply want to use a custom font everywhere in the plugin, it might be easier to force that via custom CSS:
.asp_w, asp_w * {
font-family: "my font family" !important;
}2. You can change it here: https://i.imgur.com/ZlNGazE.png
3.
a) Use the search settings shortcode to move the whole settings area away from the search bar. That type of tagged layout will definitely need custom coding, as checkboxes/radio buttons and drop-down fields are available for the filterable layouts.
b) The search icon is displayed by default for most search themes, but you can explicitly turn it on here: https://i.imgur.com/dobL0PK.png
c) Well, the closest possible feature to that is this example. You can find the related tutorial here. That uses the search settings shortcode, but keep in mind, that will move all the settings to that position. It is not possible to have multiple filters on multiple positions.
d) Using the search results shortcode you can move the results box away from the search, just like the settings box. If you only need to display 3 posts at a time, you can change that under the limits panel.
e) By using a template with a horizontal layout – that one is very similar to your exact needs.
