Thank you for reaching out.
Based on your question above.
Does azure firewall support east-west traffic filtering or it should only be used for north-south traffic filtering.
The answer is Yes although the recommended method is to use Network security groups for internal network segmentation and filtering, as documented here
"However, configuring the UDRs to redirect traffic between subnets in the same VNET requires more attention. While using the VNET address range as a target prefix for the UDR is sufficient, this also routes all traffic from one machine to another machine in the same subnet through the Azure Firewall instance. To avoid this, include a route for the subnet in the UDR with a next hop type of VNET. Managing these routes might be cumbersome and prone to error. The recommended method for internal network segmentation is to use Network Security Groups, which don't require UDRs."
In some doc I read for inbound http & https we need to use web application firewall.(Application gateway)
This will regarding TLS inspection feature of Azure Firewall
Azure Firewall supports Outbound TLS Inspection and if there is a requirement for Inbound TLS Inspection like to protect internal servers or applications hosted in Azure from malicious requests that arrive from the Internet or an external network. Application Gateway provides end-to-end encryption and should be used for Inbound TLS Inspection
You can go through this article to understand different scaneraios where Application Gateway can be deployed with Azure Firewall.
Hope this helps! Please let me know if you have any additional questions. Thank you!
Please "Accept the answer" if the information helped you. This will help us and others in the community as well.