As exhausting as it is, nothing you mention is really outside of normal behavior for a newborn. Some feed more often than others, and my own son was in the 'every 2 hours around the clock' club as well. This can seem overwhelmingly intense especially during growth spurts, which happen frequently in the first months of life. Wanting to be held pretty much always, needing to have the pacifier held in their mouth, and spitting it out even when it is wanted is also normal. Newborns just don't have the muscle coordination of their bodies and mouths to avoid ejecting the pacifier/teat.
Some babies like to drink smaller amounts frequently, others with fill up with a larger bottle and then go longer without a feed, and this seems to come partially down to habit, and partly to personality. (My own opinion and that of my son's doctor is that it's best to follow your baby's feeding cues even as it is difficult on parents, rather than try to enforce a feeding schedule at such a young age, but this is not a consensus-- some doctors do recommend feeding 'by the clock', and I would never say you should take internet advice over your pediatrician's direction.)
I don't think you need to be overly concerned about the temperature, either, if it is within the range that adults find comfortable. Babies have survived in a wide variety of climates for a long time before central air and heat were invented. Generally it's fairly normal for a new baby to have cold hands and feet, even when they are not overly cold, because of their immature circulatory systems. A touch on the back of the neck is a more reliable indicator of how warm or cold your baby is feeling. Occasional trembling/shivering is also in the realm of "strange but normal newborn things", and is more related to excitement or just the developing nervous system than temperature. It can also indicate low blood sugar; a baby that is very hungry!
Here's an article that happens to mention most of your concerns: Constant hunger, cold hands and random trembling: https://www.parents.com/baby/care/newborn/12-things-no-one-ever-tells-you-about-babies/