Is this the right time to start switching to Salesforce's new Lightning Web Component model
It's time to start learning it, but you can't use it in many typical use cases, so Aura will be viable for the foreseeable future.
(Is this perfectly compatible with Lightning Aura model, Lightning Data Service, Lightning Design System Currently)?
LAC (Lightning Aura Components) can't be used inside LWC. This limits the use of LWC to widgets that you'd place in supported contexts, and only if you don't need any LAC within your LWC. LDS and SLDS are supported, it's mostly just DOM incompatibilities.
Will Aura Component model be completely depreciated and then removed?
There are no plans at this time for deprecation. Aura will be viable for the foreseeable future.
and in future release I will have to move to LWC model having no Aura components supported?
Eventually you will want to migrate to LWC for performance and security reasons (it is far more secure and supported by browsers), but there will not be an immediate need to do so.