Need advice for a new project

The customer currently has an app build with Symphony 3.4. The current set-up is too complex to maintain, user unfriendly and not flexible, lags a maintainable SEO structure.

The main function of the app (site) is to combine client request to professional workers. As an example: a client has a leak in the sink and is looking for a plumber.

Process steps:

1. Existing or new client fills out a form (registers himself as a
   user), selects the category of professionals he needs, suggest a
   date for the fix, describes the problem (texarea) and uploads one or
   more photos showing the issue. This is in fact an order without a
   price.
2. The admin (a person in the back-end) decides which professional
   (professionals are signed up via a separate process, and are also
   registered users) fits best. And couples the clients order to the
   professional.
3. An email notification is sent to the pro. The pro logs in to his
   account, accepts the order to be accomplished at the date given by
   the client. Adds a quotation (single price field) and a description.
4. The client receives an email notification that his order was coupled
   to a professional and is requested to login and accept the quotation
   given by the pro.
5. Once accepted by the client the pro fulfils the order at the date given.
6. The pro logs in to his account, adds a photo and time of the job
   done. Uploads the invoice(.pdf).
7. The client gets a notification, logs in, pays the invoice (using stripe: cc and PayPal)
   and is requested to give a rating from 1-5 and a comment on the job done. The order
   status is set to fulfilled.
8. The pro is notified that his invoice is paid and is able to see the
   rating (not the comment) for his work on this assignment.

There’s a whole lot more but this is the core process of the system and we lacking a bit of experience specifically there.

So the question is can this be handled in Craft alone? Craft Commerce seems to have some of the functions available but expects a product/order price (in our situation the price is only set later in the process). Is a dedicated plugin needed to accomplish these tasks?