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What plugins do you have installed, how many people, what are your server specs, provide your server.log too, provide your forgelogs as well.
Then we can see what is causing lag.
There is almost nothing you can do, however that processor has many cores and as long as you don't have a load of crap running in the background you should be able to run client and server at the same time on seperate cores.
It will be fixed soon enough, sometimes happens. However there are no commands on any server to auto install mcpc. You may be thinking of some hosts providing a auto install feature with their service which just downloads it for you from that link.
What do you mean you don't have a way to shut down your server? /stop will save everything and shut it down or as long as the server doesn't save during a backup you can do it while it's running just fine.
I don't think your host is very good, even if they didn't know how to fix it google will have a answer as your not the first to have a issue with multicraft, try this https://forums.bukkit.org/threads/error-crashing-my-server-pls-help.116016/
Post this in tech support, not server tech support.
However I can tell you "can't keep up" means your CPU is having a hard time handling minecraft and that i5 isn't the best CPU for heavily modded minecraft.