It's not the number of links that would make google 'suspicious', it's the pattern. If something on your site goes viral, gets on the first page of digg, gets linked on blogs and forums, you can quite genuinely suddenly get thousands of links in a couple of days - but they won't all have the same anchor text, they'll come from a mix of sites and types of sites, and they'll be sites that are compatible with your your niche. Google has data on millions, trillions of sites and their backlinks, they know what a natural pattern of linking looks like
That depends on the size of your site and how much traffic you currently have. Sometimes when someone has a special promotion they can get quite a few links in a day. Google may sandbox you for a few days but you usually recover in a short time. Just keep it natural looking depending upon your traffic and you should be fine. 20 or so per week should be fairly safe. I get much more than that per day sometimes when talking n the forums.
link velocity is not real. Image your site has no traffic and all of a sudden your on opera and your links are exploding like acai berry's. The news determines typically who and when a large amount of links are coming and good can not predict it. Get as many links as you can as fast as you can.