The halacha (Orah Hayyim 677) is that a guest must contribute a perutah towards the fulfillment of the mitzvah of lighting Chanuka candles. I would like to know why we don't find a similar idea by other mitzvot? For example we don't say that a guest at Sukkot needs to contribute a perutah so that he has partial ownership over the sukkah he is eating in.
The gemara in succah 27b says that one does not have to own the succah to fulfill his obligation as the passuk says
כל האזרח בישראל ישבו בסוכות
With chanuka candles, there must be candle(s) lit for each household. This is the meaning of נר איש וביתו (shabbos 21b). When candles are lit for a household, all who are associated fulfill their obligation. A visitor is not considered to be a part of the household in which he is staying. He is considered a separate household. Therefore, he does not fulfill his obligation as part of the hosting household's lighting. If his wife or someone from his household is lighting, he fulfills his obligation with them. If not, he must light himself. If he can't or doesn't want to, he can fulfill his obligation by partial ownership of the candles being lit by his host. (See mishna berura or aruch hashulchan in OC 677 for most of the above.)
You are correct about the halacha about a guest contributing a perutah towards the Chanukah candles. And interesting enough there is a דעה in the גמרא (we don't paskin like this דעה) but there is a דעה in מסכת סוכה who says that a person isn't Yotzeh residing in his succah unless he owns it. So contributing to the succah would be like having a חלק of the succah. However since we don't paskin like this דעה we cannot use him as a proof to your question. However the answer I believe is that the guidelines for the mitzvah of נר חנוכה was set up strictly by the rabbis who said that a person has to sell the clothes off his back to be Yotzeh the mitzvah! Chazal doesn't say that about נר שבת or נר יום טוב. So if you have to go to that extent then surely you must have a חלק in the candles by contributing a perutah
The halachah is that everyone, man or woman, must light a menorah. If you're a member of the household then you're included in the person lighting, if you're not, you can contribute a peruta to be included. By suka, the halachah is that you must live in a Sukah, not own a Sukah. I know you gave Sukah as an example, but that was the only example you gave. What's another example, to 'hear' the shofar?
Just to note, some people, like Lubavitchers, have the minhag for all males to light their own menorah.