If I buy ArcGIS Pro, do I need to buy Spatial Analyst and 3D Analyst extensions separately, or do they come free with the package?
If you already have ArcGIS Desktop (ArcMap) with those extensions, ArcGIS Pro is licensed to use the same extensions - you won't need to buy the extensions again.
You will need to set up your ArcGIS Pro Extension licenses in the same way as you set up your ArcGIS Pro licenses.
Can I use my licensed ArcGIS for Desktop extensions with ArcGIS Pro?
Yes. Since ArcGIS Pro is part of ArcGIS for Desktop, you are licensed to use the same extensions for ArcGIS Pro as you are with ArcMap (as available). The following extensions are available for ArcGIS Pro: ArcGIS 3D Analyst, ArcGIS Spatial Analyst, ArcGIS Network Analyst, ArcGIS Workflow Manager, and ArcGIS Data Reviewer. The extension licenses for ArcGIS Pro are managed using the same method you have chosen for your ArcGIS Pro license.
Just like with ArcGIS for Desktop (that you'll receive if you buy ArcGIS Pro and vice versa) extensions must be purchased . Note that with ArcGIS Pro, you'll be able to visualize layers in 3D (but you won't have access to the tools of the 3D Analyst toolbox if you don't buy it).
For both Desktop applications, you can evaluate any extension during (I think) 2 months for free.