Accommodation directory possible?

- Multiple images per accommodation / entry will be published?

Yes, as many images as you want. You can determine how they are displayed. You can determine if the entry is published immediately, or if it goes into draft status.

- Can I create as many fields as i want?

Yes, there are no limitations within Gravity Forms.

- Can the running time of publication of entries to be limited?

Since you are talking about posts here, this is something you would need to control from within WordPress. You would have to expire the post. This is not something that Gravity Forms does. You would need a plugin or a bit of custom code.

- If yes, how are admin and user notified?

If you're talking about admin and user notification when a post is created (form is submitted) these notifications are built in. If you're talking about notifiying an admin and a user (person who submitted the post) then this too would be part of the WordPress plugin. When the post is marked as expired because time has run out, you would need to notify some people.

- What kind of search and sorting capabilities on the website have the visitors?

This too is built in to WordPress. You are creating WordPress posts using a Gravity Form. Nothing more. All the functionality for display, search, sort, post status is all built in to WordPress.

Gravity Forms will create the post. After that, it's up to you what you do with it.