Hi,

1) I need the registrations to be extremely customised

You can try free version to understand how it work.

2) I need the search options also to extremely customised

What do you mean "extremely"?, You can set each field to become searchable and for each menu item you can choose which field show in search form (instead a menu item search form you can also create a module with searchable fields). In the latest release we have added also backend search feature.
Keep in mind that Easy Profile is mainly a profiler extension and not a directory component.

3) search only post registration.

You can set Joomla Access for module and menu items, so you can manage who can access to various parts.
For example you can create 2 menu items
- List User (without search) for guest members
- List User (with search) for registered members

4) display the profiles in a particular way.

Easy Profile is written with Joomla MVC model, you you can customize output with Joomla override feature (you can try this on free version)