Usually servers are never configured with cheats (with exception for Defrag/Training servers at times) but if you are not sure, then a good, and easy, way to check is to type:
(for example) and if you get all weapons from start, then chances are that you play on a server with cheats. Your ping does not really matter, it all comes down to what you are comfortable with. With that being said, it is easier for someone with a ping of 15 to hit with a railgun compared to someone with ping 350, but both are equally possible. Nut in short, yes: lower ping = less lag.
Use the 'lag-o-meter' to check how your network is configured for the game, a more detailed explanation of it you can find here:
http://gameadmins.com/modules.php?name=Sections&op=viewarticle&artid=5One thing you can do to try and improve your ping is through settings. Now, depending on your hardware/network configuration, these numbers might vary, but try something like:
/snaps 50, /rate 25000 and /cl_maxpackets 125
. Good luck and welcome to the game.