What it does is it singles-out a religion. That religion happens to be Muslim, and the countries happen to be countries that have a high concentration of Muslims. That marginalization (or discrimination if you're a potential jihadist) makes it easier to recruit people into their terrorist organizations. The more they recruit, the harder it is to overcome.
If the objective is to have fewer potential terrorists, this is not a good idea.
Nope. No Islamist group uses immigration as a means to recruit new members.
The reason why these 7 countries are named is because they refuse or can't help with the vetting of their citizens. How do you determine whether somebody is a potential threat without their country of origin providing background information?