If you're doing road riding then I would take the plunge and use road shoes and pedals. Shimano, Look, Time, and Speedplay are the main pedal companies and offer a pretty wide selection of products across different price ranges. All of the companies mentioned with the exception of Speedplay use a three bolt pattern which means the cleat is triangular in shape and the locking mechanism is located on the pedal. Speedplay has a rectangular cleat but has the mechanism located on the pedal. While all cleats have float (the range of lateral movement your ankle can travel), Speedplay offers the most float. This is important for people with knee issues as their foot/knee alignment isn't as restricted.

You will need road shoes. Sidi, Specialized, Lake, Giro, and Shimano are some companies to look at. Go to a shop and try some on as some shoes have narrower toe boxes than others and you want to get something that fits correctly to avoid foot issues in the long run. If you decide on a pair have someone at the shop set them up because getting the cleat alignment correct is important and harder to do alone. The cleat attaches to the bottom of a road shoe with screw, the cleat in turn is locked into the pedal using a spring system which secures the shoe to the pedal. Turning your ankle outward releases the cleat from the pedal.

It depends on your intended use. If you're looking to use regular shoes and aren't interested in road shoes then toe clips are the way to go. If you're looking to ride for fitness then clipless pedals are the way to go. Road shoes have a stiffer sole which prevents energy loss by the bending of the sole of your shoe which is what happens when you use sneakers or other soft soled shoes. Being clipped in also makes it better to pedal in circles meaning you push down and pull up during each pedal stroke.

Yes but this depends on your intended use as well. If during or after your rides you plan on doing plenty of walking then perhaps MTB shoes/pedals are the way to go; they're better than using soft soled shoes and toe clips but the pedals have less surface area and generally speaking the soles of MTB shoes aren't as stiff. I know quite a few road riders who opt for this and it works fine for them. Personally I prefer road shoes and the benefits that come from using them. There are also MTB pedals which have a standard platform pedal one one side and an clipless mechanism on the other. As for walking in road shoes it only becomes a problem if you're going to walk a good distance. Walking around a short distance hasn't been a problem for me as I have cleat covers to protect my cleats and provide some traction. If I plan on walking around then I put some flip flops in my jersey pocket...during the summer of course.

Yes you flip the pedal up and clip in. Practice makes perfect, this is especially true of pedals with one point of engagement. Once you use them enough you'll know exactly where to place your foot to clip in without looking. Speedplay has two points of engagement meaning you can clip into both sides of the pedal while Crank Brothers Eggbeaters offer four points of engagement but sacrifice a good stable pedal platform (note: Eggbeaters are MTB pedals). I've been using single sided clipless for a long time so I sometimes clip in faster than some folk using standard platform pedals.