The P38 was produced in large numbers during and after WW2.
Sometime in the 1950s (if I remember correctly), the design was
updated slightly, and the pistol redesignated the P1.
Since production of the P1 continued all the way into the 1990s, I
would definitely consider it a "modern day pistol." 
Does "military surplus" means it was never issued for
service? It look like mint condition.
Milsurp firearms might or might not have seen actual usage. It
is entirely possible that there might be crateloads of brand-new,
unissued firearms sitting in an arsenal at the time they are
declared obsolete.
Milsurp firearms sold in this country are usually graded and priced
according to their condition, with the unissued ones commanding the
highest prices. However, a batch of used milsurp firearms might
occasionally have some unissued example mixed in with it. Such was
the case with my particular P1. 
(If you look real close at the images, however, you will notice
some very minor scratches on the finish. Though a milsurp firearm
might be unissued, it will almost always exhibit some minor
handling wear.)
How much is such a piece worth? As a comparison, how
much is, say, a standard 92F?
The worth of a milsurp firearm can vary considerably based on
such factors as when and where it was manufactured, its physical
condition, historical significance, and availability. Using the
P38/P1 as an example, a P38 that was made in WW2 and actually used
by the Wehrmacht could fetch well over US$1000, whereas a P1 that
was manufactured in the 1980s for the Bundeswehr (but never issued)
would be worth no more than about US$250.
A brand new Beretta 92FS can be currently purchased for around
US$550 at the retail level.
What's its performance like in terms of reliability and
accuracy? The 92F has a large mag capacity compared to the Walter,
which means a bigger grip.
Is the barrel longer than on a 92F?
For a military-issue sidearm, the P1 is surprisingly accurate.
My particular example will print a sub-3" group at 20 yards when
slow-fired offhand. I have not put a lot of rounds through it as of
this writing (I would estimate no more than 500 of my handloads),
but it hasn't burped or jammed on me thus far.
The P1's magazine holds 8 rounds, while the 92FS can hold either 15
or 16 rounds (depending on the magazine manufacturer), so yes, the
grip of the 92FS is necessarily larger.
Both the P1 and full-size 92FS have barrels that are approximately
4.92" in length.
Sorry, so many questions.
Hope I answered most of them to your satisfaction.
