Your first question is somehow difficult to answer, but to do so, you should answer the question "How confidential your data is?".
When you use a service like sharelatex, in some point they are going to host your data. Even though they say your data is being hosted on secure third parties, still some one else is have your data. Now, am I telling you they are going to read your confidential data? No.
They point is, when a third party is hosting any type of data, theoretically they can read or use it. If you use google to email them or dropbox to share them, they are still on those companies' servers. You do not hear or read news about hosts stealing scientific ideas (or perhaps they do!), but you do hear news about your data not being exposed. In particular sharelatex has one problem that their privacy on this matter is not that clear:
ShareLaTeX uses third parties to host our services and store your
data. You retain all rights to the data you upload to ShareLaTeX.
Which brings us to my first question again.
How confidential your data is?
If you have solved P vs. NP or any a Millennium Prize Problems, you better not to go with sharelatex (or dropbox or many other services for that matter).
Before going to your second point, I would like to emphasis that I have not used their service and what I wrote does not question their honesty, integrity and quality of their services. I just suggest not use it when your data if of extreme confidentiality.
So what to do? There are so many solutions. First, if you really like share latex, they are now open source and they do encourage you to fork their code. You can make your own sharelatex and host your own data (their git repo).
Another solution are subversion or git. I have used both git and svn for single and multiple author works and both are fine. You can use them on your own servers or use online hosts. As you guessed correctly, the latter has the same problem as sharelatex, however, a host such as github is already hosting many closed source projects and you know you are not alone in this boat. But again, if you need ultimate security, you should host your own data. To read on trustworthiness of online repositories read 1,2,3.
By the way, as mico suggested in the comments perhaps you should find the source of the problem. If you decide to go with one of the online repositories yet use you own machines to compile the latex source, you eventually need to look at latex with
platform independent glasses. If you and your collaborators use same versions of latex and avoid using obsolete packages, you should not have any problem. To put into perspective, recently we finished a paper that was written on Linux, Mac and windows.
I have two final notes regarding online latex service like sharelatex. Firstly, by using their services you have to give up some of your freedom. What if you want a non-standard latex package that is not supported by your online engine? You are only the lord of your own garden! Second, despite of all I said about security, in many cases, Source code is worthless.