Seems like the remote is a must, so really this will cost another 80 bucks...?

The remote is waterproof but has the same function with GoPro app in smart devices. You decide if it worths 80 bucks but for me yes i bought it and used it so much in water.

Does this include the remote control and waterproof case?

No remote included, however the free GoPro app is more useful then the simple remote that is a separate purchase where the app is free, the silver standard edition at least (not the music or sport models) comes with the clear case with three back doors that make the case either non waterproof or water proof to a certain degree, the skeleton door allows easier use of the touchscreen but is not waterproof, then touchscreen back door is only good for 10 meters or 30 feet, and then the full waterproof back door is good for 131 feet which is perfect for scuba and other deep diving scenarios, where the touchscreen door is good for snorkeling and free diving to 30 feet, I hope this answers hour question

does the battery charger come with the camera, and if not, how do you charge it?

It comes with a usb charging cable, you can charge the camera by computer USB port or you can use most any other usb wall charger from smart phones or other types of usb devices used by things like cameras, usb accessories, smartphones, iPhones or multi port usb chargers.. I bought a nice little four port usb charger for my phones and other items that charge by usb and it charges the camera pretty fast, I bought it here on Amazon and it works for all my usb devices so check it out, it's pretty inexpensive, I think I paid $15.00 to $20.00 for it and it works great for all my usb devices

Just ordered this camera. What else do we need to order to make it minimally functional for an upcoming vacation? How many hours does battery last?

Wow hmm good question, for starters I'd order a desktop battery charger, I ordered a dual bay small desktop charger that came with a spare battery and the charger and a USB Cable, and the dual bay charger also has a third pop up charging port specifically for the GoPro remote, so get that and order one more spare battery so you'll have a total of 3 batteries, I'd also order a couple extra SD cards and a multi accessory pack that has adapters and accessories for underwater filming, selfie sticks, floatation buoy mount and a case to hold it all, and quite a few more items including a case to hold it all in so those would be the base setup that would probably cover most vacation moments with spare parts and extras you might need in a pinch, I mean it's more then you probably would need but it's nice to have them just in case and with a total of three batteries you could film pretty much all day for 8 to 12 continuous hours of video or possibly more? and then the extra memory cards are the equilivelent of spare video tapes for a standard video camera so hope this helps you or someone else, the nice thing is you can get an accessory pack and a case and spare batteries for maybe an additional $60.00 or a bit more depending on how much you want to spend you can get more items for less or fewer items for more money? But if you shop around you can get the most bang for the buck

Brand Name	GoPro
Item Weight	5.1 ounces
Product Dimensions	2.8 x 2.79 x 1.53 inches
Item model number	CHDHY-401
Batteries	1 A batteries required. (included)
Is Discontinued By Manufacturer	No
Color Name	Silver
Special Features	Waterproof

Hero4 Silver

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