I'm no expert but have given your questions some thought. Here's my $0.02:

I presume you want to model your data to derive some statistics or probabilities based on the sample you have collected. From your description your data does not appear to be normally distributed - there are a number of

tests to confirm this. I am unaware of a multi-modal distribution that will "fit" your dataset as described - but why not just generate one yourself. The idea behind any statistical distribution is that the area beneath the probability density curve is one. You could generate a model with multiple humps that correspond to the peaks in your dataset e.g. a fourth order polynomial function could work. The integral of this function over the range of your dataset must be such that it equals 1. You can then use this function as the statistical distribution of your data.