Stock Air cleaner box...
 

What are the hoses connected to it for? Do i have to keep them or can i take it out?

You can remove them if you remove the air pump and the entire rats nest. They are for emissions and since you live in cali, I dont know if you should do that or not.

why are emissions so strict in california?

Because Californians are special. I live in Iowa, home of no emissions testing WOOT. If you get pulled over for loud exhaust, they give you a fix-it ticket. If the look and see if you have no cats, I am sure the fine is crazy but reeally all you gotta do is say that you are having carb problems and have a hole in your 20+ year old exhaust.

CAn you remove it if you still have the air pump and rat nest?

If you have any hopes of passing emissions, leave it alone. The only benefit of the rats nest removal is a couple of hp from removing the air pump and the cats need to be removed too. If you disable the air pump, and leave the cats, they will be short lived.

You do not want to know the cost of replacing the stock cats to pass emissions. These days, it can exceed the purchase price of many of the 1st gens.