I don't have anything that can tell me the exact age from the serial number, but I've heard that the Roman-style Serif lettering was phased out in the early 1920s. Later FN Browning 1910s have Sans Serif lettering.
If you're not familiar with European pistol cartridge nomenclature, FN 1910s marked "7.65" on the barrel are chambered in .32ACP; those marked "9M/M" are chambered in .380ACP.
FWIW if the pistol is a .32, magazines are currently available for $12.95/ea from IMA-USA. Get 'em before they're gone!
BTW make sure you order the 7rd 1910 magazine,
not the 9rd 1922 or 1910/22 magazine; since these pistols use a European-style latch on the butt, the longer 1922 magazines will not lock in place in the shorter-grip 1910 pistols.
http://www.ima-usa.com/belgian-browning-1910-7-65mm-fn-magazine-7-rounds.html
If the pistol is a .380, you can modify .32 magazines to work; the only differences are that there are 6 cartridge-counting holes rather than 5, and the feed lips are slightly narrower. The width of the mag body and the mag follower is the same, and the mags are actually often totally interchangeable in practice. If not, a little filing and bending to the feed lips will fix any problems.
If the thumb safety will not hold the slide back, the second notch in the slide probably needs to be cleaned up with a small triangular file; this seems to be a common problem with these guns. If the safety won't operate with the slide pulled back, it's probably because you're depressing the grip safety and locking it; it's supposed to do that. It may take practice to draw the slide back without putting pressure on the grip safety.
BTW these pistols are wonderful shooters, although the teeny sights can make them hard to shoot accurately beyond contact range, and the grip safety makes the grip position awkward for people with large hands; I have to hold them slightly sideways to put enough pressure on the grip safety for the pistol to function reliably. Due to the small grip, I actually shoot these pistols better using a one-handed hold; the other hand just gets in the way, and the recoil is mild enough that I don't need it.