no extremely rare Pokemon live in lilycove city, but you can get hardish Pokemon from there, and there are some rare Pokemon that live on the route on the west of it.
you can get staryu by fishing on the beach with a super rod, but its quite hard to come across one.
there are some rare Pokemon in the safari zone.
when you defeat the elite four, latias/OS (depending on the game) can be found on the grass on the route to the west of it.
and that's about it! :)
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team aqua hideout at lilycove city
go to lilycove city then to mossdeep city then to pacifidlog town and not any other
The Team Aqua boss is in the Team Aqua Hideout northeast of Lilycove City. You will need the HM move Surf to reach the hideout.
In the Department Store in Lilycove City. Basically in other Pokemon Marts, too when you have enough badges.
The Magma Base doesn't exist in Sapphire Version, but the team Aqua's Base is located outside of Lilycove City.