Question regarding stop codon
Yes, this is still considered mRNA. A lack of stop codon is usually due to a so-called readthrough mutation, where DNA sequence changes within the stop codon and after transcription it can no longer be recognized by release factors. But yes, ribosomes still recognize the mRNA molecule and start synthesizing abnormal proteins, usually until the ribosome stalls on the 3' end of mRNA and can neither go further nor detach. There are various mechanisms converting this "stalling signal" to a chain of intracellular reactions that lead to degradation of that protein and that abnormal RNA.

Bacteria for instance have a very curious mechanism of solving that problem, namely a tmRNA molecule that is targeted to a stalled ribosome by some specific proteins and acts as an aminoacyl-tRNA as well as mRNA template. It resumes translation, allowing addition of a peptide tag to the malformed protein, which will serve as a marker for degradation. More on that here:
https://en.wikipedia.org/wiki/Transfer-messenger_RNA
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3358797/