When customer places an order, will the vendor get an email with order details or not?

Yes, the vendor got a notification via email when the customer placed an order for a particular seller's product.

Basically, this is a default functionality that is available in our marketplace, for this admin must allow the Seller Manage Order as 'Yes'.Now the seller can generate invoices for their ordered products, generate a tracking number and shipment for orders of their products.Even the seller can notify the customers by sending them emails, cancel/refund the order and even print the order.

Please refer to the below screenshot for the mail notification template on behalf of the vendor end : 

Please do contact us for any further queries or requirements. You can also check our Magento 2 Extensions for additional features.