can we use a saved search as a source for a select (List/Record) or multi-select field? if no, what's a valid source?

In script, say on a SuiteLet Form, yes, with some work. If you are defining the field via UI look at the sourcing and filtering options.

@NElliott could you please explain how can we do that on a suitelet form?

perform the search, add select options where the record id is the id in the list and the text value is another column from your search

many thanks