I'm Egyptian, have Swiss C residency and a US visa and would like to see my sister who is living in the US and traveling to a third country through the UK. She has a long stop there in Heathrow transit and I would like to meet her there. Will they let me board the airplane in Switzerland? I.e. is it allowed to travel to a country (in this case UK) without planning to enter the country (which would require a visitor visa and I don't have time to apply for one)? My sister and me would just meet in the transit area. Thank you so much for your help!
This is not generally permitted, at least not without doing something more. Timatic, the database airlines use for immigration requirements, states that transit without a visa is only allowed for transits "on the same calendar day to a third country (excluding Ireland (Rep.))." Flying, say, ZRH-LHR-ZRH is not a trip to a third country and would not qualify.
You could engineer your trip so that you do end up in a third country to satisfy this requirement or try to buy another ticket for that purpose.
Note that Heathrow has four different terminals. While it is possible to move between them without crossing the border, it normally requires a boarding pass valid for that terminal. It is also theoretically possible to book a personal shopping service to take you to another terminal. Otherwise, you'd need to ensure you book flights that will get you into the same terminal where your sister will be waiting.
If you want to fly Switzerland-UK-Switzerland, you need to buy a "throwaway" connecting ticket from the UK to somewhere where you don't need a visa (which includes any green/yellow country in this map, but also, thanks to your Swiss residence Permit, several others such as the CEFTA countries (except Moldova), Turkey (only Istanbul-Atatürk airport), Georgia or Mexico) in order to board the flight. This should be a full-fare ticket, so you can cancel it and get a full refund.