You do not need a license/permit to carry to purchase a gun...maybe in some states, but not here.
Here we have a 48 hr waiting period, whether it's by a private seller or dealer...while the application for purchase with the buyer's & seller's info is sent to the local and state police. The seller is also required to keep a record of the purchase on file for 6 years.
I still believe if a person is going to kill someone they will find a way regardless of the methods available. We just had a nutjob stab someone and run into Target when they chased him...he grabbed a 16 yr old girl standing at the checkout and started using her as a shield, stabbing her 3 times puncturing one lung. We could argue the variables until hell freezes over...if he used a gun or a bomb he could have killed more people...or if someone had a gun they could have shot his stupid ass in the leg before he ran into the Target and grabbed the girl and wounded 4 others...or maybe he could have tripped in one of Pittsburgh's massive potholes and fell on the knife while running to Target. You can rewrite the script a thousand times, it may or may not change the outcome.
As for being "responsible enough" I don't think there is any fool proof method of ever determining that, I know people who aren't "responsible enough" to breed, but they have.