Deer hunting is an ongoing learning experience. You have asked some good questions, it shows you are concerned not only with killing a deer, but with responsible action after the shot. I wish you had an experienced partner to hunt with. But let me caution you, good hunting partners are hard to come by. If you can't hunt with someone who has the same convictions as you do, you are probably better off going at it alone.
That said, I'll try to answer some of your questions, according to my experience. Pay very careful attention to what happens after you shoot. If you can get another shot, do so until the deer is down, or you can no longer see it. If you see the deer go down, you are lucky. If not, be sure to note everything, such as how did the deer react to the shot, the direction of travel, and a compass heading of the last sight or sound of the deer. (I've found that a compass heading is especially helpful when hunting from a treestand in thick woods, as everything looks different when you get back down on the ground.) If the deer bucks up and runs off, it could be a gut shot, and you would want to wait several hours before following up. If it akes off like a jet, in a straight line, crashing through everything in front of it, with its tail tucked, probably a good boiler room hit. If you find a blood trail, and have to trail the deer, the most important thing I can tell you is TAKE YOUR TIME. I use flagging ribbon tied over each spot where I find blood if it is sparse; this way, if the trail dries up you can look back, see the trail the deer was making and have an idea of what direction to keep going. Trailing is probably the hardest part, for someone who hasn't the experience. But this is great experience which you will have forever after you learn it, and it will be that much more rewarding when you find your deer.
What to do next depends a lot on the temperature. If it is warm, as it is often where I hunt, gut the deer immediately, skin it and rinse the blood off the meat ASAP, and get it on ice, or at least hung and covered with a sheet or bag which breathes, but will keep flies off it. If the air is cooler or cold, say 40 or below, you have more time. Gut the deer as soon as is convenient, and you can hang it, for days even. Hope this helps you. LOL