With an SOIC chip, I don't worry about "order": I just hold tweezers on the chip, blow some hot air, and it comes off in about 1 second. What you're describing is orders of magnitude more difficult and time-consuming.
Thank you for this thread, as it makes my fussing with soldering today to fix some shorts in a couple guitars (my own fault from poor soldering years ago) sound quite pedestrian so I should aim to do as best as possible, cuz y’all out here be doing advanced EE projects!!
Yes, definitely, if they're really close together. But "loosening up" isn't a problem with SMT; as long as the legs are adhered to the pads with the proper amount of solder, it's correct. The risk is moving adjacent chips around so they're no longer properly centered on their footprints, so using the hot air gun does require some finesse: use enough heat and air velocity, combined with the distance of the tool to the board, to remove the chip you aim for, without affecting the adjacent chips.