Hello and thank you for contacting the Toolset support.
I would like to integrate Facet WP in order to do the filter of the propoerties and Toolset. Can I use both things together?
Well, this is a rather general question and my answer would be Yes and No.
Short answer
Yes, you can use both plugins. And no, you won't be able to use 100% features of both plugins.
Long answer
FacetWP is a search plugin whereas Toolset plugins offer a wide range of features, the search included. FacetWP search is custom made(uses internal database tables) and relies on WP Core, and third-party plugins stores(Relevanssi, SearchWP), whereas Toolset searches are based on WordPress core+Toolset relationships+Toolset Maps.
This being said, you can still do FacetWP search on custom post types, custom taxonomies, and custom fields created by Toolset. But there are some limitations. The search may work smoothly for some types of fields(number, single line, multiline, etc.). But, may also give unexpected results for other types of fields(checkbox, radios, checkboxes, etc.).
FacetWP will interact directly with the data stored in the database. For a checkbox field as an example, it will find the values stored in the database instead of their labels(Yes/No vs 1/0). This may happen to select fields, radio fields, checkboxes fields. Because FacetWP won't have visibility on the fields labels and options, which are specific to Toolset.
Toolset does have an integration with Relevanssi for 3 fields types(Single line, Multi lines, WYSIWYG) only.
So, my suggestion is to evaluate the options of each plugin based on your site requirements. Let me know if you have a question about a specific feature or option.