I have read that SSIS performs variable lock in scripts. So when scriptA and script B use the same variable one of them will wait for the other to finish.
Still I dont know id this is the same for Connection Strings.
For example I have two HTTP Connections being used in two webservices. if they are called constantly I am testing what happens.
Your assumption about SSIS variables is incorrect. SSIS doesn't perform "semaphore" type locking on variables. It won't "serialize" execution in order to allow two scripts that use the same variables to execute without interfering with each other. SSIS will fail the script that attempts to use a variable that is already in use by another script. If you think about it, it makes complete sense - having it operate any other way invites unpredictable race conditions.
There is no such thing as a "connection string" in SSIS. They are Connection Managers. An HTTP connection manager will manage a pool of HTTP connections. But I don't understand how that relates to "locking"?