Can I sync objects such as Deals/Tasks/Invoices/Opportunities/Notes/... ?

In short, no. PieSync currently syncs data stored on CONTACTS or COMPANIES only.
Syncing Deals, Tasks, Invoices, Opportunities, ... is not yet available as these are different objects/entities from a syncing perspective. We're working on this though.
But I need this today!
Advanced CRM software like Salesforce, Pipedrive, Zoho, or HubSpot allow you to move data across objects. Bring over data from an opportunity onto the contact or company, so it can at least be used as a filter. We cannot exhaustively document how this works for all CRM's, but here's a couple of examples to inspire you.
If your need is short-term and your own software does not allow for information to be moved across objects, perhaps Zapier or other integration software can help bring over some information. Find out more.