Yes. But that is small part of the SEO. I believe you need to learn a bit more to ba able to understand that better
Yes if the link page has backlinks from bad sites it may get penalized & having your link on such site which has been penalized by search engine won't do you any good.
yes for now backlink is number one, but we don't know the future? when google change their algorithm. I hope its more easy the before
Well its true that getting a link from a bad site wont help for sure but it doesn't mean that if a bad site links to you you would be penalized if that would be true it would be very easy to beat your competition you will just have to build a bad site and link it to your competition. But this is not true. But getting links from good sites surely helps.
As far as in my experience, getting backlink from a link page is dangerous. It is not good for PR. Because, there are pages which are filled by lots of links sometimes, so, that page will become a link farm. Link farm is considered as a spammy page by google. So, google really hates a link from link farm. That may harm your SERP or PR.
Before getting a backlink from any page (not only link page) check the outgoing links. Is it pointing to any adult/porn/gambling sites. If yes, then it is a bad idea to get the backlink from that page if your site is not related to this topics. Secondly, measure total number of outgoing links per page. If it is more than 100, it is near to worthless. So, try not to waste your time on higher outbound link pages.
Getting a Back link from the links page is good. No one will give you a link from the home page unless you give him back the same advantage. So link are exchanged in the links page, its your problem to check weather the page is useful and satisfies all the specifications. Most important is that there should be a link from the links page to the home page of the site. If not it is want of time. Good Luck
Backlinks plays a big role for your site. Getting quality backlinks from relevant site will help to get top ranks in SERP. Backlinks are one among the important factors in determining the keyword ranking for your site. I suggest Social Bookmarking as the simple and effective way to get backlinks.