There is no way to reduce laggness. The only way you can is to inform your admin and he or she can upgrade the versions to reduce the laggyness
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Lag is usualy how slow the server your on. the expression "I'm lagging" means your going slow, due to the server. always wait for someone when they are lagging if you're role-playing.
use a 64-bit java to run minecraft. Or install optifine to reduce lag
the lag is controled by the type of computer and the amount of space that your computer has! Also in your games you can add anti-lag scripts that will help do that, to add that either make one or get one from free-models!
lag can't be completely avoided, but you can reduce it by going to your options, and lowering quality features, such as changing fancy graphics to normal graphics
The same way you do on singeplayer - right click the chest. However, if you are referring to a bukkit server or any server with plugins and the chest is locked, there is no way to do it yourself. This is to prevent theft and it works very well. Additionally, there may be server lag. This means that there may be a delay before the chest items appear. Do not worry, the lag will go away soon (hopefully)!