But how this should be done?
You have watched the structure of custom_fields?
You can add them to the search index, yes, there is an add-on now.
To search like > 20 years and < 40 years, you need the addons from Addonslab, but they are monsters.
Probably you require a new way of structure for custom fields to use them.
I see
a) you add a copy of the content in a searchable table
b) you put the searchable fields to the main tables
c) you add a new type of custom-fields to search in, while the old type is only to show information.