This is likely an error with WorldGuard and permissions.
1) Players cannot build. Check and make sure the area is not claimed with Factions (/f map) or protected by WorldGuard (do /rg info when standing in the region). If it is not, you need to give your players the permission essentials.build. If you're using GroupManager, this can be done with /mangaddp default essentials.build. The permission node is the same in PermissionsEX.
2) Players cannot PvP or PvE. The problem is likely due to WorldGuard. Ensure that the area is not regioned by doing /rg info when standing in the area, if it is regioned, do /rg flag <region> PvP allow and /rg flag <region> interact allow. If it is not regioned, do /rg flag __global__ pvp allow and /rg flag __global__ interact allow. Interact allows them to hit mobs like zombies and cows.
3) Players cannot use commands This is an issue with your permissions plugin. You need to give the default rank more permissions. A complete list of essentials permissions is here: http://wiki.mc-ess.net/doc/permissions Every plugin has their permissions listed on their Spigot/Bukkit page. If you are unsure how to use your permissions plugin to add permissions, or do not have one, search YouTube for a tutorial on GroupManager or PermissionsEX, and download the one that you prefer.