A hot pixel is a pixel in a cmos sensor or a lcd screen that is either not recording right or not firing right. There are acceptable thresholds within factory warranties that vary with the brand/item.
Noise is found in digital cameras, the higher the iso plus the lower the light, the more noise you'll have. Noise can be seen as grainy or off colors that don't look natural. Some cameras come with corrections for this built in, others you have to deal with it. Basically, all cameras will do some things well, a lot of things awesome, but only a few they don't do so well. Noise is in all to a certain extent, but it all depends on what you plan to shoot. I.E., buy the right camera the first time.