How could I write a function allowing users to edit a 3D object?

Question

I am writing an Android App which allows users to DIY their phone cases and then export them to .stl/other 3D printing format.

There is a function:

1. User inserts a photo(a logo/pattern).
2. my app will draw the corresponding pattern onto the back of a phone case. For example, lets say the logo is an apple. The user can choose "Hollow" or "Convex&Concave" mode.

"Hollow" is sth like this: enter image description here

"Convex&Concave" is sth like this: enter image description here

The case doesnt have any pattern on itself(plain one). So this function will draw the image onto it.

My question is:

1. How to write an editting function(allow user to edit 3D object in run-time) in Unity3D(C#)? Are there any built-in functions which could help me achieve this?
2. Or do I need to import plugin from other software(3ds max, CAD) in order to perform this function?

I am not sure if I have made my problem clear enough. If you want more details, just feel free to ask. Thank you very much!

Image source: 1. dhresource 2. tvc-mall.com