Yes disavow is the good way to deal with it and Google webmaster don't show all backlinks you should buy some other tools. I have used ahref and LRT that are fine you should buy one better backlink research tool.
It is hard me to say that if your competitors will generate bad backlinks then it will effect bad for your organic search or not.
But I think it differently why competitors will spend their time and money on it if they know how SEO works than they will work for their site, so by this they will be on top slot and they will not be worry about your site.
You do your business I do mine because you are you and I am I If we meet it is nice.