I mean, in google's eye. Aren't directories just thousands of pages with tons of links on it? Do I get penalty when I submit my sites to many small online directories?
No, that's a link farm. It's unlikely you'll be penalised for directory submissions, if that was the case people could submit competitors sites to devalue them. IMHO a directory of any kind from yellow pages to Web directories should be a place for the user to find relevant information in useful categories.
Yes. No. Otherwise your competitors will be able to ban your site and it won't be fair, right? It's common sense.
Are you talking link farms? Directories will give you legal backlinks which are accepted by google, while link farms will be penalized by google.
I don't think you can get a penalty if the link is one-way. If that were the case, then somebody could sabotage a website's rankings by adding their site to a bunch of link farms.