how to achieve search form external DB

Hi everybody,
I’m newbie in WordPress, i come from Drupal and Joomla so I’m still getting used to it.
What i need:
I have to integrate in a WP site a search form that, on one hand, list registers of an external database, and on the other hand, shows a card with the register details when i click in one of them.
I made this in Joomla, with a component for the register details page, and a module for the search form.

How can I achieve this in WordPress?
I suppose i need to build a plugin, or a widget, for the search form so i can place it in different areas.
For the page with register details maybe i have to create a template for that especific page and put there all the PHP/JS/etc code. I choose a page, not a widget, because I need that each register has an URL (…./bla.php&id=777 or similar). Can i achieve this with a widget, maybe i can access url params within a widget, i don’t now right now…

I’m mistaken in something? There’s another better option?

Ok, and now suppose that i want to have the search form (with the result list aside) and the register card with the details below, all in the same page. Can I avoid creating a plugin and do all the staff in the template? Is easiest this way?

I need to shed some light on please.
Thanks!