Lets start with the regression side of the problem:
Given that you want to place constraints on your coefficients, you're going to need to use Optimzation Toolbox. The constraints that you're describing a pretty simple, so you should be able to use lsqcurvefit.
With more complicated constraints, you'd probably want to use quadprog instead.
Let's move onto the multicollinearity question:
I'd start by using something simple like a scatterplot matrix to visualize the data, and follow up by calculating some simple summary statistics.
If you determine that multicollinearity is a problem, your best best will be to wrap the sequentialfs function from Statistics Toolbox around lsqcurvefit.