b) PostgreSQL's full text search is quite capable but not so powerful that it can completely replace Lucene-based systems. So you have to consider complexity vs functionality if you are tying with other data that is already in PostgreSQL. Note further that my experience with at least ElasticSearch is that it is easier to scale something built on multiple PostgreSQL instances into the PB range than it is to scale ElasticSearch into the PB range.
c) Solr or ElasticSearch
One question about your use of PostgreSQL for a TB-scale full-text search system: Did you order search results using ts_rank or ts_rank_cd? I'm asking because in my experience, PostgreSQL full-text search is extremely efficient, until you need ranking. It's because the indexes don't contain the necessary information for ranking, and because of this the heap has to be consulted, which implies a lot of random IO.
Check out the RUM index extension, it adds ranking information to indexes to speed up exactly the problem you pointed out:
