String models of particle physics 
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*What general features of particle physics are derived/replicated by constructing string models of particle models? 

*How do such models address the fixing of free parameters like the masses and the coupling constants in the Standard Model?
I have a little bit of background knowledge of string theory, having studied the first part of Zweibach's book, but except from attending some talks on AdS/CFT correspondence and the string landscape I don't know much about it.
 A: While a very important question, I don't think my answer can do much justice in attempting to explain a gargantuan open problem in theoretical physics. But I can give you some overview and point you in the right direction.
As of now, everything is work in progress. There are a lot of issues with the standard model which current experimental data cannot validate such as why three families of fermions, why are there so many free parameters etc. What string theory needs to do is that it must provide a consistent formalism in which a 10 dimensional supersymmetric theory can yield a gauge theory (which can in principle reproduce the MSSM) coupled perturbatively to Einstein-Hilbert gravity in 4 dimensions. We know that string theory reproduces EH gravity. 
For particle physics constructions, there are three highly followed methods as of today:
a) Calabi -Yau and orientifold compactification
b) Model building from D-branes
c) F-theory
I would suggest the book by Uranga and Ibanez on String Theory and Particle Physics which is very good and caters to the interests of a grad student to an experienced researcher. 
One of the key ideas in string theory is to obtain the correct compactification from a 10 dimensional supersymmetric theory to a 4 dimensional non-supersymmetric theory. A very interesting avenue for this is the study of Calabi-yau manifolds for which a read of the excellent review by Brian Green is recommended. 
Finally, there is F theory. I wont go into the details of F theory here but there is a very nice review by Timo Weigand on F theory and model building. 
All these methods show a lot of promise and there is a lot of work being done in these areas but the questions that you are asking are still work in progress. The hope is that one can derive a model from string theory in 10 d a model of some gauge theory coupled perturbatively to gravity such that the gauge theory can explain the obtainment of the parameters in the standard model. 
I would also recommend the lectures by Frederik Denef and Elias Kiritsis and references therein. 
All in all string theory is still yet to recover the standard model but it is work in progress. 
For a set of elementary introductions, I would recommend these notes by Jan Louis, and some notes by Fernando Quevedo which can be found here and here. These two people are two of the most influential string phenomenologists. 
A: "What general features of particle physics are derived/replicated by constructing string models of particle models?"
All of them. Essentially every field-theoretic property or phenomenon of the standard model, has a string-theoretic realization.
"How do such models address the fixing of free parameters like the masses and the coupling constants in the Standard Model?"
In principle, such quantities are determined by the choice of vacuum. For example, if a gauge field is realized by a brane stack, the coupling may equal the volume of the branes. But in practice, the ability to compute them is still limited. 
