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Good morning chevra,
The coming week's Mishnayot are very rich and varied. I'll point out three ideas that I hope will be interesting and useful, and acknowledge that there is so much more here!
(1) The issue of "sending portions / gifts" (1: 9 and 10) is interesting. The sending of gifts, in particular but not exclusively gifts of foods, is assumed to be central to the joy of Yom Tov. (This served, in fact, as the inspiration for Purim.) The only halachik concerns that arise are the following: (a) "Carrying". While "carrying from domain to domain" is broadly permissible on Yom Tov (as we saw back in 1: 5), the item being carried needs to have some kind of Yom Tov utility, even if that it utility is fairly remote. But items that have no Yom Tov utility at tall cannot be carried unless there is an eruv. (b) It is possible that depending on the nature of the items, the transfer of gifts could appear to be - or could in fact actually be! - a commercial transaction of some kind (in which case even an eruv wouldn't help. These are the factors that are being weighed out in the Mishnayot.
(2) Mishna 2:5 establishes a principle that goes well beyond the one example that it discussed there. Bet Shamai, very reasonably, understands that the Torah permitted the melachot needed for food preparation only if we are actually doing them in the course of food preparation. Thus, boiling water that could only be used for washing purposes would be forbidden. But Bet Hillel believed in the sweeping principle that "once a melacha has been permitted due to its food-preparation utility, it is permitted for any beneficial utility." As you see, the Mishna extends this principle to lighting a fireplace (using a pre-existent flame) simply for warmth.
(3) Mishna 7 teaches the one major caveat that applies to the rule just discussed above. The Sages objected to Rabban Gamliel's use of fire to burn incense because "any beneficial utility" doesn't really mean any beneficail utility. The utility in question has to be one that most people enjoy on a regular basis. The burning of incense however, was a rather aristocratic practice. Here's a good article (about showering on Yom Tov) applying this to our modern day: https://www.daat.ac.il/daat/english/Journal/broyde-wagner-1.htm
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