To be honest, if your asking these questions, are you ready to take on a security project? Is English your first language?
I'll give it a shot:-
A PROXY server, is one that acts on behalf of others to provide a service. I am assuming that you are talking about a PROXY server for internet access? This is a a decision that is outside of having a domain controller or not. For example, a mobile phone on your internal wifi network, is not going to authenticate with active directory. (unless your have some very strict IT policies, which if you did, this question would not be here :) )
The domain controller and the firewall do not have interactions as such, unless you want to provide services to computers outside of your physical network, for example, if you have an exchange server, and wished to provide access to OWA - then there would be some interaction between the domain controller and the firewall (port forwarding probably, but even then, this is network behavior, not domain controller behavior).
When you say manage the laptops of people going to customer sites, I am assuming that you are talking about connecting via a VPN? This is a new question! I can answer that here, but I'm making a big assumption, because MANAGE is such an open word, how do you manage your systems as it is? (very big question) - Ask in a new question, it's free :) "How do I manage remote workers, who are using company laptops?"
Outlook is not dependent on having a domain controller - although you can increase your productivity within Outlook, by having an EXCHANGE server. I believe this is what your question is about. Again, maybe ask a new question - "What are the benefits of having exchange in an environment with lots of outlook users?"