Manual transition occurs when you specifically transition from 1 stage to another using Change Stage smart shape. Conditional transition occurs when you specify a condition for when this stage should be transitioned into. Automatic transition is the default, i.e. once all the step in a stage is processed, it automatically transitions to the next stage.

Not too sure what a "procedural" stage is though. Can you clarify where you get this term from?

Alternative stage does not allow automatic or conditional transition, so it can only be manually transitioned using Change Stage.

In your child case, you can configure the "Instantiation" option in the Details tab of the Case Type in the Case Designer. You have various choices of automatically starting the child case by the system, via conditions, or manually starting the child case, also via other conditions. I suggest opening up the Case Instantiation dialog in the child case to have a look at the various options available.

Please read these up for more information: 

https://pdn.pega.com/sites/pdn.pega.com/files/help_v718/procomhelpmain.htm#tools/casedesigner/casewideproperties/instantiation/tsk_configuremanualinstantiation.htm

Thanks for the reply..i got confused in procedural instantiation of sub-cases.Can you state in how many ways sub-case can be instantiated? Does procedural instantiation (i.e) through activities or data transform is possible?

From the available Activity methods (https://pdn.pega.com/sites/pdn.pega.com/files/help_v718/procomhelpmain.htm#methods/index.htm) I do not see any OOTB way to instantiate a new sub-case.

However, there are available Pega APIs there allow you to create new cases (https://pdn.pega.com/sites/pdn.pega.com/files/help_v718/procomhelpmain.htm#pega_api/pega_api_about.htm)

I would suggest you go ahead and test things out. One of the best ways to learn. Let us know how your tests goes.