Yes, to the second paragraph, no for the first paragraph.
At the moment there are about 10,000 refugees who are coming every week to Germany, can you tell me how Germans could check every one of them? In some districts (lands) there is very difficult situation, there is too many migrants and it is impossible to check all of them. The same situation is at present in Sweden.
What's more, only abt 30% of migrants come from Syria. Many of them come from Afghanistan, some from Iraq, some from Ethiopia and other African countries. And majority of them are males, 25 to 35 years old, only 2- to 30% of the migrants are women with children.