Let's take the questions one at a time. If the magazine safety won't move to allow the magazine to be inserted, field strip the gun and look at the little plunger that sticks out of the back of the recoil spring guide. It may be stuck in the rear position. It activates the mag safety and if it can't move, the safety can't move forward. If that is not the problem, then the magazine safety itself may be stuck and get back to me on that.
If the plunger is stuck, try loosening it with a good penetrant and some pressure. The spring is heavy, but the plunger must move freely.
Now for the second problem. I assume that in that case the magazine won't enter at all or only with a lot of pressure. If the mag safety is not a problem, check to make sure you don't have a .32 pistol and a .380 magazine. Many people think they are interchangeable but they are not and the guns are different. Even some magazine makers have tried to make a common mag for both calibers; some are too large to fit a .32.
Jim