Conditional logic & form styling

1) Conditional Logic can accomplish this. You would have to add ALL the questions to your form and then use Conditional Logic to show/hide individual fields based on previous user selections.

2) Yes, you could apply custom styles to those questions. However, you would have to write the CSS to do so. You can apply a custom class to a field and then target that class using CSS. You can also view source on the form and see what id's/classes are used by default and use them to target the fields with CSS. Gravity Forms uses standard HTML and CSS so you would style it just like any other page element.

3) You can customize the form however you want with CSS. However, you will still want to use the base Gravity Forms stylesheet because the forms are entirely styled by CSS so if you don't output the Gravity Forms stylesheet you would have to handle all of the styling yourself. We recommend keeping the Gravity Forms CSS output turned on and simply adding custom styles to your theme stylesheet to override the default styles using CSS inheritance and targeting.

4) Currently search capabilities are limited to a free form search box that searches all fields. There aren't currently any search filters. However, we do plan on implementing an Advanced Search capability in the future.

You would place your custom CSS in your themes stylesheet. If you edit the Gravity Forms plugin stylesheet your changes would get overwritten when an upgrade is executed, so it's best to place changes in your theme stylesheet.

Gravity Forms does not currently use FieldSet. If you want to use FieldSet you can use the HTML field and implement it yourself if you know what you are doing with HTML.