This is usually known as a Mauser 1910 or 1912. The 6.35 stands for 6.35mm Browning, which is the ammunition it takes. In the USA, it is called 25 Auto or 25 ACP (Automatic Colt Pistol - the first gun here made for it was a Colt).
In Germany the gun was also called the Neun-Lader, I think, because the magazine held nine rounds.
It is much larger than the usual 25 caliber pistol, which makes it more pleasant to shoot but underpowered for its size, especially by today's standards. 25 Auto is about as powerful as 22 Long Rifle, but it feeds and ignites more reliably.
They were made starting in 1910, revised in 1912 (yours is the revised version) and made until the mid or late 1930's. They sold pretty well, so they are not rare, but Mausers are heavily collected, so it has reasonable value. I don't know enough to estimate it, tho.
Mauser was one of the most prestigious gun makers in the world, so workmanship and materials were first rate for the time. The design is rather complicated, so I don't remember the take-down method offhand.
The little pedal by the trigger is the safety catch. You push it down to engage it, and push the little button to release it.
This website has a good article about these guns:
PS - Thanks for putting up pictures!
PPS - Mauser also made a larger version of this design, in 32 Auto (7.65mm Browning in Europe). It is usually called the Model 1914, with a modified version called the Model 1934.