I could not find information in the documentation about whether the shards are filtered during a SELECT query if the filter of the query includes the CLUSTERING KEY.
will the engine skip the shards that do not contain c1=55 or will it still search all the shards even if their distribution was based on this exact field?
Additionally, I am interesting in the equivalent question with the partition key instead. Will only the shards of one partition be searched in this case?
For partitions it is definitely taken into account. You can check that by running your queries with EXPLAIN ANALYZE. This shows which shards are queried.
How it exactly work with only the routin_column being set in CLUSTERED BY I would have to check.
Generally if you are interested in how CrateDB works I can recommend you the excellent articles from @mfussenegger