If you use Postgresql's query engine on the Clickhouse data, you lose all the benefits of the columnar query engine of Clickhouse so that's not correct.
No you don't lose them. Fdw supports push down of where clauses, only selects the required columns.
You can also create views in clickhouse to make sur the joins are processed there.
You're right but if the syntax that you're using is not supported in Clickhouse, aggregate and predicate pushdowns won't work and this FDW (https://github.com/adjust/clickhouse_fdw) needs to map all the Postgresql functions / produces to Clickhouse in order to take advantage of push-down so the only use-case here is that you may want to join the data in Clickhouse with the data in Postgresql (or other FDW sources).