Congrats and welcome to the RV community and this forum. Yes you can opperate the slide on just the battery but if you can plug into a 20 amp household circuit so the battery stays charged up. The trailer converter should do this automatically. Now you have to remember to check the water level in the battery every so often so put it on like a monthly check list. Now you will need varying adaptors for plugging into different recepticles so pick up an adaptor that is regular duplex to 30 amp plug like that is on the trailer. Pick up a 50 amp to 30 amp adaptor for campgrounds that only have 50 amp service plugs. You say you already have the surge protector so that's good.
I keep my sewer hoses in a bin. Find some bins that will fit into your storage compartments and then you can collapse the slinky to fit into it. I get 30 ft. into one bin with the connection fittings and caps. I put my outdoor cooking pans in a bin and put electrical cords and outdoor lights and lanterns in another bin. I have basic tools in another bin....categorize your bins for the things you store.
As you camp you will find out the things you need to have. Don't over buy stuff. You will end up with a bunch of stuff you find you don't use or need. Seeing that we can't really go anywhere yet read your manuals. Learn about your new trailer and its workings. You did right by getting the 4 point Equal-I-Zer hitch, its a good hitch. Read that book too on how to keep things torqued and lubed properly. After all that you will be ready to go have fun.