Hi @YugandharG ,

1. Lakebase data is stored in databricks-managed cloud object storage. There's no option to use customer storage as of now.

2. File format: vanilla postgres pages. The storage format of postgres has nothing to do with parquet/delta. Watch below video where Reynold Xin explains how Lakebase works under the hood and how they achieve separation of compute and storage. Really interesting talk.

Introducing Lakebase - Databricks Co-founder & Chief Architect Reynold Xin

Of course Lakebase support synchronization of delta and iceberg tables but the data itself will be stored in postgres tables (which are supported by postgres pages). 

3. Currently there's no direct way to query Lakebase table using REST API. But you can manage your database instances using REST API. Here's a list of all activities you can perform through rest api:

4. I don't think so. At least I couldn't find any information regarding this in documentation.