I think you have several possibilities. But I would try the following: to extract the information of coding sequences from a gtf or gff file, and the do the mapping. The reads that remain unmapped are those you have not interest either because they do not map, or because they map to genes which you are not interested

In relation to the second question. The quality of your mRNA reads don't have to be affected by the method you isolate the RNA. If you are asking for how good is a population of poliadenilated mRNA when you do a total extraction compared with when you use oligo-dT , I cannot answer with confidence, because I am not experienced not I read a paper comparing both methods. I believe however, that there is a global acceptation the total RNA method is valid when a method a suitable and effective method for getting rid of the ribosomal RNA is present, and this is a obligated step for procaryotic organisms where I never heard a complain

You can give that for sure.. You can map to a reference genome with all genes, and count only those reads you are interested based upon a annotation file that only contain your coding genes of interest

You can use whatever annotation is available for and relevant to your assembly, though keep in mind potential issues. For example we have seen cases where certain RNAs (e.g. miRNA) change in a global way with some treatments, which directly breaks the assumption that most normalization procedures have, namely that only a small group of genes change.

Other 'harder to work around' issues include draft-quality annotations with little evidence for gene calls. In those cases it may be worth going the reference-based assembly route (Cufflinks or Trinity), then running DGE analysis. This way you try to capture as much information as possible, though even in the reference-based assembly case you are still reliant on a genome assembly which is hopefully trustworthy.