Does the concept that we find by Hotza'ah, "if you are Matznia (Machshiv) something then you are Chayav even on a Kol Shehu", apply to other Malachos as well. For example, if I am Machshiv a little piece of food and want to cook it, will I be Chayiv for Bishul because of my Machshava?
There are two separate kinds of being Machshiv that we find by Hotza'ah. One type is being Machshiv an item which has two purposes, and for one of the purposes amount A is Chashuv, and for the other amount B is Chashuv. This is also applicable to other Melachos, as stated by TOSFOS (76b, DH "ha'Motzi").
It is unclear to me whether the other type of being Machshiv by Hotza'ah, where a person is Machshiv a small amount of something that people are not normally Machshiv, is applicable by other Melachos. A certain Talmid Chacham suggested to me that based on RASHI (144b,DH "k'Rav Chisda"), where Rashi says that even if someone in the world designates something as a liquid, it can create a Chiyuv for Sechitah, so too if someone was Machshiv something which is Chashuv by certain people, that person can be considered Chayav. However, most Rishonim argue on Rashi (see BIUR HALACHAH O.C. 320, DH "Mutar).
Of course, we are talking about a Chiyuv Misa. Almost everyone would hold that even doing a small amount of any Melachah goes into the category of Chatzi Shiur Asur Min ha'Torah.
You raise a very important issue. The Mishneh l'Melech (Shabbos 18:21) explains that the din of "Kol Shehu" applies only to the cases mentioned in the Mishnah: planting, sample and medicine. They are the exception to the general rule of shabbos, since there is a minority of people do who use a Kol Shehu. In any other case however, even if a person is Machshiv a Kol Shehu for himself, we consider this Botla Da'ati Atzel Kol Adam.