I suggest not immediately. Wait until you have much more specific evidence. For example, you say 'a lot of exercises'. I think you should specify two or three of these at least. Are they perhaps really meaning 'one' rather than simply 'a'? In which case it is incorrect to omit it. Hope that helps.
I am familiar with the difference between "one" and "a". I am pretty competent in Latin and Ancient Greek, so it feels unnatural always using an indefinite article. "A lot" means that in most review sessions I hit at least one. They may be the same one, even. The next time it happens I'll report… It's probably just a few that were overlooked and it feels like more to me subjectively.
Nothing obvious. Wiktionary says etymology is uncertain: https://en.wiktionary.org/wiki/%CF%80%CE%AF%CE%B8%CE%B7%CE%BA%CE%BF%CF%82#Etymology