Can you download photos from a camera straight onto a tablet?
It depends on the camera and the tablet. Most (but not all) Android tablets have an SD card slot so if you have an SD card in your camera you can pop that in the tablet and get the photos that way. Some tablets have a USB port so you can also use a USB card reader. Otherwise you can upload your pictures via a PC to a cloud service like Dropbox and retrieve them on the tablet.
Is there much difference in display quality between brands?
Yes. The key thing to look at is the screen resolution. Although there are other smaller factors which make a difference too. Some top end Android devices have better resolutions than the iPad. But also, a lower resolution on a smaller screen will also be sharper so look for the ppi (pixels per inch) figure. Anything above 250 will be pretty nice above 300 will be stunning.
What's the battery life like and what happens when it starts failing? Can you replace the batteries?
Battery life depends on the tablet. Some, such as the Asus Transformers which have batteries in the tablet and the keyboard can give you 15 hours plus, but check the spec. Generally they are not replaceable but a tech shop may be able to do that for you. However it's not something you will likely have to worry about in mid to high end devices for several years.
Is everything done by an app, or can you access the internet through a firefox type program?
Everything you use on a phone, tablet or PC is an app, application or program. They all mean the same thing. Tablets will come with an Internet browser. This will either be the standard Android browser or the manufacturer's own. However, Firefox, Chrome, Opera and Dolphin along with many others are available to download for free.
Take your time looking at reviews online. Many cheaper tablets are a false economy. They are made with cheaper parts, slower processors and less memory. But you could do a lot worse than a Nexus 7 for under £200.