Hello to everyone, I’m a fresh new user of ZBrush, and I find this forum very alive. Being a user of 3dsMax and photoshop I have to think a bit differently in ZBrush, by reading somes topics in this forum I have an almost clear view of what can be and what can’t be done but I know I 'll have a lot of questions as I’m going to use this amazing programm.
So I have a newbies question. After creating an object, I can change it’s resolution density with ‘Initialize: H & UDivide’, is there a way to see in the viewport the wireframe of this object( temporarely) to have an idea of the number of faces created and as long as this object is not collapse does the subdivision can be change. And when I place a copy of my modified object by choosing it in appear in the Tool palette, does this new version can be subdivide too and does all the copy of an object share the same division attributs like if they were instanced or are they independente.
In the preferences palette click the DOTS button on. You’ll see wireframe when you move the model. 
Kathy already answered your question , but I’d just like to say welcome to the board and if you have any other questions about Zbrush feel free to post them in the Zbrush Forum , You’ll get more answers and probably quicker 
I would like to echo The Namek, and welcome you to the Forum…There are lots of great people here to help you over the learning curve we all experience with ZEE, and we’re all glad to help! 
thanks, first question settled.
Can I subdivide locally, ex: the bottom of a cylinder, and can I do bolleen operation with objects
think I found a part of my question, ZCut substract one object to another, but how can I add object to another
What is the difference between ZSub and ZCut?
To subdivide locally just paint a mask on the area to be divided by holding down the control key. Then in the Tools>selection invert the mask then divide.
you must be in draw mode to paint a mask if you are in move edit mode then you will draw the current alpha as a mask.
Sub and cut are the same for the 2.5D tools.
for the 3d the difference is that Cut is like a boolean subtract. And Sub is like placing a hot bar on an ice cube, it sort of sinks in cutting its way through.
IMHO cut should be called sub and vice versa.
when I save my document does it snapshot the 3d object?
Well you can find that out easily enough, try it and see 
To edit a tool from one session to the next you must save it in the Tools>Inventory>save.
Tools cannot be saved in the Demo version.