First of all, citations are not synonymous with links, although a lot of citations do include links. A business citation is just a mention of the company, often in a structured format and including the address, phone number, and website (but not necessarily).
Secondly, you'll need to clarify if you are referring to local search results (3-pack, 7-pack etc with map) or the organic search results. Citations (with or without links) have the greatest effect on local results. They help search engines distinguish one business from another, particularly in local search and map results.
Your question implies that citations only have value inasmuch as they help your website perform in search. On the contrary, business citations help customers find the products and services that they need online, even if they never make it to the company's website. In fact, it can be extremely frustrating to customers when they can't find what they need online, as I recently found out. Citations can be highly beneficial in terms of "Barnacle SEO" as well.
To answer your questions:
1. There are typically about 50-100 general and niche citation websites that are important for each industry. Anything beyond that will see diminishing returns.
2. Links from citations can be beneficial to an entire site, for the most part, but they are more significant for the target page. Avoid citations from spammy sites.
3. Citations are one of the biggest factors affecting local search results. See the 2014 Local Search Ranking Factors.