It isn't necessary to boil your milk, but if you prefer, then the cream will have a different consistancy, and it may reduce the amount of butter, not sure though, because we never boil ours.
If you let your milk cool in the cooking pot or a bowl the bigger surface area makes it easier to skim. I think the tea pitcher idea is a good one, but I haven't tried it.
That weird pudding skin consistancy is normal. Take the cream you have skimmed, and the amount you are getting is fine to make butter, and put in a glass jar with a screw on lid. You don't want the jar to be much more than half full. Then give it to a child to shake. THey will shake until their arms are ready to fall off, then pass it on to someone else. Your cream will first turn into whipped cream, you can stop there and use your whpped cream, or you can keep going. As you are shaking, all at once you will feel the consistancy change back to a liquid and see little globs of butter floating in there. Keep shaking and the butter will clump together.
At this point you unscrew the lid, drain off the liquid (use for baking, or my fil loves to drink it) rinse the butter a few times in cold water right in the jar and pour off. Then you get the butter out (wide mouth jar or mayonaise jar works well here) and put it in a bowl. Take the back of a wooden spoon and mash the butter against the side of the bowl to squeeze as much liquid out as possible (the liquid is what goes rancid first, so the more you remove, the longer your butter lasts) then your butter is ready! You can shape it into a sort of log and wrap in plastic wrap, or you can put it in a container, but it will get hard in the fridge, remember that. Your butter is going to be white, instead of the yellow you are used to. It is really very easy. If you want salted butter, add the salt after you squish all of the liqid out and it is still soft.
Once you have made it with a jar a few times to get the hang of the consistancy changes, you can experiment with your blender or hand mixer. The older your cream is, the quicker it makes butter. I hope this helps, if you have more questions or something doesn't make sense, I would be glad to help.