How does bulk API utilize active threads of write thread pool?

How does bulk API utilize active threads of thread pool? I have an index with 1 shard and 1 replica. When I push , say 100 documents, using bulk API to this index, will it employ 1 thread of write thread pool to do the ingests?

Roughly speaking, yes, each bulk request is processed by a single write thread on each shard.

My indexes have 1 shard and 1 replica. Does this mean one thread will write to both the primary shard and its replica?

No, that can't happen: the primary and the replica are on different nodes, so they are in different processes and normally on different machines. There's no way that a single thread can do both writes.