If I was hired in January and my contract expires and will be renewed in July, should I expect a salary increase then or at the end of the year like everybody else?
In contract work your compensation is one of the terms and can only be (re)negotiated when your contract is (re)negotiated.
should I expect a salary increase
No, you should not expect it; you can try to negotiate an increase when and if the contract renewal is offered to you.
Under the contract you are a vendor of services to the other party. Why would your client be expected to pay more for the same services just because some time interval has passed?
I would expect it when a new contract is being drawn up, if at all. And maybe it wouldn't even be when the first six month contract expires but maybe it'd be when the second six month contract expires (since that'd be a year later).
Ultimately, I think it'd probably depend on the reason why you were on a fixed month contract anyway. Like if your company was doing defense work and they, themselves, had received a six month contract from the US government to work on some project, then whether or not your contract would be renewed or include a pay increase would depend on if your employee had their contract renewed, budget increased or staffing requirements reduced.