The answer to both of those is "yes". When you configure the live copy, you set up a "live copy config" file. Basically all that contains is a mapping that says "when I live copy this thing, I want to change this property value to this other value". More specific to your questions, you would add an entry that changes the sling:resourceType of certain components to (what I'm assuming) are more mobile friendly ones. You would do the same for page nodes and the properties cq:Template and sling:resourceType.
In fact, what you are describing is part of why MSM is very powerful. The config is a little tricky to set up, especially if you start using wildcard operators, but you should be able to accomplish what you want.
Thanks Ryan, it seems promissing.
Can you please provide a reference from documentation or a package where I can see it in action?
I don't remember exactly where the documentation is, but I know docs.day.com has some good information about it somewhere.
I tried some googling but couldnt find anything regarding "live copy config" specially in connection to swaping template and components. Can anybody point me to right direction?
Look at /etc/msm/rolloutconfigs/geometrixx-outdoors-mobile. There are examples of this config (called rolloutconfig, not livecopyconfig - my bad) in CQ.
For everyone else interest URL is
Edit properties (copied)
On the live copy, it edits properties of the live copy: the selection of the properties and their transformation is done by setting a value to the editMap property. ...
See one of my earlier response thread http://forums.adobe.com/message/4894991#4894991
Goto "etc/msm/rolloutconfigs/mobile/_jcr_content/editProperties" and see the values for "editMap" properties to update template name during Live Copy. Like wise you can modify some of your properties during livecopy.
editMap : [property 1]#[current value (regex)]#[new value (regex)],[property 2]#[current value (regex)]#[new value (regex)]