Clarification of the procedures to amplify cDNA needed
Here is the rough procedure that I've used to prepare cDNA before


Extract RNA from desired tissue (select for mRNA using the polyA tail of mRNA)
Conduct reverse transcription. This requires a primer complementary to the polyA tail to get the reverse transcriptase started (Edit:You could also use random primers to prime reverse transcription. This eliminates the redundant polyT sequence from the cDNA. This is the method used in the Illumina TruSeq high throughput sequencing library prep kit). Now you have a collection hybrid RNA/DNA double strands
Digest the RNA strand specifically. This can be accomplished with RNAse H as you mention, or by introducing basic conditions, which degrade RNA much more rapidly than DNA due to the 2'OH of RNA. Now you have linear ssDNA complementary to the inital mRNA templates.
From this point your applications may differ. If you are doing microarrays, all you need is ssDNA, since you want to hybridize the cDNA to the array. If your downstream use of the cDNA requires dsDNA, then you need to synthesize a complementary strand to the cDNA (and potentially amplify the product). This can be accomplished through PCR random primers, or some more complicated PCR that will incorporate extra sequences on either side of your cDNA (e.g. bar-codes and adapters in RNA-Seq). 



  How is [the cDNA] protected from the nucleolytic activity?


If you are digesting the product of reverse transcription with RNAse H, that enzyme digests RNA specifically, so your DNA is unharmed. If you are going with an alkaline conditions treatment, then the RNA will be degraded in those conditions much more quickly than the DNA due to the presence of the 2' OH group in RNA which can act as a nucleophile for a self-cleavage reaction.