Buy it.
Yes, the R.E. means Italian Army. I'm not familiar with "F.A.G." with a crouwn. I'll try to do some checking if I have time. Regardless, it's well worth the $150 if it looks good and there's nothing wrong with it. The 1934's have been going up in price lately, but they aren't going crazy. A gun like you describe is probably in the $200-250 range. It's a good time to get one, as it's only a matter of time before collectors drive the price up on these gems.
The 1934 is a very solid gun, and is overbuilt for the .380 round so they tend to last forever. Workmanship is great on them, even the wartime production ones. They're simple, reliable and tend to be very accurate, even with those crappy sights. For a small gun, it fits your hand quite well and is very comfortable. Wolff sells a replacement sping pack, and it's worth installing if you're going to shoot it. As a blowback, it's a good idea to replace at least the recoil spring in a 70 year old gun just in case.
As 73stick notes (welcome BTW and great first post!), I'd hesitate to carry it with a round up the spout. The safety is not the best desgin, both in ergonomics and how safe it really is. I'd echo his thoughts on carrying it chamber empty.
They're nice guns, and you'd be hard pressed to find a better .380 even after all these years IMO. It's a nice piece of work.