What is the Toolset Pack limit to do so?
There is no limit enforced by Toolset for the number of Custom Post Types or Content Templates, as far as I know, but working with a massive number of post types isn't going to be very practical in WordPress, even without Toolset. WordPress's wp-admin area isn't designed to be optimized for a massive number of custom post types. The main menus aren't easily managed or consolidated, and each of those 1000 post types will be created as main menu items. A 1000 item menu isn't really usable, you could spend minutes scrolling through the menus to find the item you want, and the browser performance of an HTML page with 1000s of items like this may be poor.
Another example, when you create a custom field group or custom taxonomy in Types, you will have the option to assign that group/taxonomy to one or more custom post types. This interface will have hundreds or thousands of checkboxes with no organization or filtering, and is better geared towards sites with fewer custom post types. Similarly, the dashboard at Toolset > Dashboard lists post types and provides information about their templates, fields and taxonomies. When the number of CPTs gets very high, this page may perform poorly. Site performance will always be affected by the amount of content in your database.
Is there any special setting modification required (like max_input_vars etc.)?
You will very likely need to increase your max_input_vars settings, as well as your memory limits.
How can I easily manage them in WP backend? Viewing, searching, filtering, displaying their relations etc.
Toolset doesn't provide many options for organizing or managing the menus in wp-admin, so each custom post type will be added to the main menu. If you want to consolidate or organize those menus, you'll need to look for another 3rd party system that provides that capability. Searching for custom posts in wp-admin is similar to searching for standard posts. You can go to the Dashboard for that CPT, where you have the ability to use a standard text search, date filters, sorting by title and date, and post status filters. With custom code, you can add other filters to these admin Dashboards.
To see information about post relationships in general, you can go to Toolset > Relationships.
Each post editor screen contains post relationships editors for each possible post relationship. If a custom post type has hundreds or thousands of relationships with various other post types, then the post editor screen will be difficult to use. It's not optimized for a massive number of post relationship editors, and these are not paginated or searchable.