monday.com can absolutely be used as a CRM to manage both your sales pipeline and client database. Each item can be a lead/client and using different columns, you can add any important information. You can group your boards based on the different phases or you can do this using status labels.
Check out this article which might be helpful: https://support.monday.com/hc/en-us/articles/115005311909-monday-com-as-a-CRM?abcb=89539
You can also contact firstname.lastname@example.org for more details on how to get setup!:)
Yes, each item on the dashboard or each deal in the pipeline can be assigned to a person who owns or works in this lead. You can work on the leads assigned to you which is having your own crm. In your dashboard you can customize it the way you want it to, it can be on the deals you manage and their status or numbers.