I dont like to comment on specific details because I simply don't know what works and what doesn't.
The best thing you can do is look at what is ranking and do your own version of that. If it's currently ranking well (and has done for a long time) there is a very chance that google likes it. But bear in mind that sites with very high link juice and brand awareness can get away with stuff that your brand won't be able to.
If it was penguin you won't get a links warning.
If you have been hit by panda or penguin a reconsideration request wont help.
I would totally redesign your homepage. I don't like looking at it at work, it feel almost like a porn site. Plus the there are nearly 70 h2 headers which feels spammy and there is very little content.