This is a question for the geoprocessing forum, but I'll go ahead and try to answer it here.
ModelBuilder run order is controlled by the processing chain of inputs and outputs. For example, if you connect the output of one tool as input into another tool, the tools will run in the proper order.
In situations where there is some ambiguity as to the tool run order, you can use "preconditions" to control the sequence. This is described in the help - just search for "precondition".
As for your licensing question, that's a question for the ArcGIS Desktop - Installation/Configuration forum. Your license level should not be modified by an update from 10.0 to 10.1.
Hope this helps.