P1 and P38 are both correct, based on who they were made for. Post war P38s were all stamped P38 up until 1957~1963 (dependent upon source cited). Most collectors will give you the 1957 date. At that time the German military began stamping their guns P1 and using that terminology. Civilian models continued to be called the P38 and stamped as such.
Sight adjustment is with the front sight only. Try and drift the rear sight, you will damage the cover on top of the slide. Don't remove this ~ they are easy to damage and the gun should not require that level of stripping for normal cleaning.
The P38 was designed to shoot the 124 grain FMJ standard velocity round. A lot of shooters are using the 115 grain FMJ Winchester White Box with great results. Stay away from heavier bullets, plus P rounds, or putting heavy spring kits in the weapon.
Late Upgrades: Not a deal breaker ~ but nice to have if you got one with them.
Hex Bolt
The hex bolt was installed to give the locking block something to ride on rather than the aluminum frame. One needs to keep in mind that thousands of these guns were in service for decades prior to the hex bolt and saw no problems. Most in private collections will never be shot enough to manifest a frame wear problem.
Fat Slide
The "fat slide," is identified by the longer battery of serrations that extend forward of the safety lever. More early Walther P38s had problems with cracked slides over frame problems. Walther beefed up the slides to correct that.
A couple of sites to do some good research are:
http://www.waltherforums.com/index.php
http://forums.p38forum.com/forums/index.php
