I've not printed a case, but I have done a little 3D design and print.
> 2/any recommended (free) software I can use (blender does not like me)
I use FreeCAD. It takes a bit of learning and it helps if you have 2D drafting experience, but even then the concepts of extending that to 3D require quite a bit of new thinking. Use YouTube tutorials, or even better see if there is a local college doing on-off introductions to 3D (I found one very useful). You should not have any problem with scale, and I wouldn't recommend Blender for engineering jobs (it's more of an artists tool).
> 3/suggest any good reliable sites that will print ?
I have had work done through https://www.3dhubs.com/
. Be aware that service providers may just be hobbyists at home trying to make a little money out of their domestic 3D printer, but professional outfits may well be a lot more expensive. If you can pick up somebody locally to you, you may be able to arrange to go and see it happening or have the odd trial-and-error.
> 16cm*10cm*2cm sound good?
Should be, but the larger it is the fewer providers you will be able to choose from and the more expensive the print will be.
> 5/would the build thickless controlled by the print or do I have to specify?
The design is not flat like on a piece of paper. The design files will explicitly state all the wall thicknesses, and that is what will be printed (there is a minimum thickness of course). You are designing the shape of a volume, and the volume has to be explicitly bounded form all directions (even from inside). If you miss something out, the design won't "compile" (ie produce a printer output file from the design file).
> 6/how sturdy are 3d prints ?
I have four holding the hub caps on the wheels of my car - I needed adapters when I changed the alloys but wanted to keep the original caps (which no longer fitted). Just don't make the walls less than maybe 2mm thick (3mm would be better).
> 7/will I also need to add temporary support structures too?
Only if you need overhangs. The item is printed from the base up, so any "horizontal" surface should be the first thing printed otherwise it will need something to support it. Typically you would design a box to be in two parts: the base and four sides, and then the lid (which you would print upside down). If you want to print apertures, you will need a support structure in them, but the compiler may add these for you automatically. This is where an introductory course comes in handy.
> any other advice ?
Yes: Don't dive in at the deep end. Start with something simpler. Alternatively, look around for an existing ready-to-print open source design file.