1. It depends how PODS saved the content type, but I suspect that will be in the Database, just as Types, and not hardcoded.
Hence I would recommend creating the same types, fields, etc in Toolset and then use the WordPress export/import Tools to migrate the actual contents.
https://toolset.com/faq/how-do-i-convert-existing-custom-types-and-fields-to-types-control/
https://codex.wordpress.org/Tools_Export_Screen
2. For this you can use the Toolset Forms Plugin, its features are elaborated here:
https://toolset.com/documentation/user-guides/front-end-forms/
For specific questions related to forms, please open a new ticket with just one question/topic each ticket.
Please see https://toolset.com/toolset-support-policy/
3. That's possible only with Custom Fields where you upload from the Computer and not from the media Library of Toolset.
There are however development works ongoing to actually allow to use the Media Uploader in Front End forms - later then we can further detail this development to let users control more details about what media is visible to whom, but there is no current solution to this in Forms and no ETA for a release changing this.
As well here, if you have specific questions please open one new ticket for it.
4. Possible with Toolset Forms as in #2
5. Possible (with some limitations) as in #2. You will create a Post Relationship first with Toolset Types, then you will either create a Form to add Child Posts and there select one parent, or, you will create a Relationship Form where you can connect 2 Posts at once (but no more)
The DOC I linked about Forms will lead as well to that topic.
As well here, for clarifications, we need one ticket.
6. Elementor is integrated with Toolset and documented here:
https://toolset.com/documentation/user-guides/using-toolset-with-elementor-page-builder
Please pay attention to this one but crucial detail:
https://toolset.com/documentation/user-guides/using-toolset-with-elementor-page-builder/create-templates-for-custom-post-types-with-elementor-and-toolset/#limitations-when-using-elementor-and-toolset-templates-together
As well here we need another ticket if anything needs more clarifications
7. For this, you will require Toolset Views, and build a Custom Search with it. These features are all explained here:
https://toolset.com/documentation/user-guides/display-lists-of-posts-and-create-custom-searches/
In case you need more details about how to create a View or Search please refer to the policy of one ticket each issue.
8. I think Toolset has as well a solution for this one last goal.
https://toolset.com/2018/11/introducing-toolsets-communication-system-for-professional-listing-sites/
How to: https://toolset.com/learn/how-to-create-a-messaging-system-with-toolset/
It's available as a Module, for that you'll need Module Manager and download it: https://toolset.com/documentation/user-guides/using-toolset-module-manager/
Again, for details and further tailored help in regard, one ticket/issue would be required.
I hope this helps to start and organize the plan of action, please feel free to ask us anything in case you get stuck or something's not clear.