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When meaty/dairy/treif food is cooked in a pot, the taste (ta'am) of the food is transferred to the pot. When the pot is reused for other food, that food becomes meaty/dairy/treif as well. Likewise, food residue on an uncleaned knife can affect other food cut with the same knife.

Does this apply to ever min hachai?

Meat from a live animal is cooked in a pot, and that pot is reused for other food. Is that food forbidden to non-Jews? If a Jew eats it, is he liable for ever min hachai specifically or only for eating treif in general?

Does it depend on the specific type of transfer (absorption of taste, residue on a knife, etc.)?

On the one hand, I'd expect that if a pot can absorb the taste of meat or non-kosher meat, it can absorb the taste of ever min hachai in the same way. On the other hand, I've never heard of such a restriction, and Noahides don't seem to worry about it in practice.

This is a great question, which is debated by two of the great Acharonim. The gemara in Sanhedrin 74b considers that specific details of Jewish law might apply to Bnei Noach when they intersect with their mitzvot, since they are included in the "associated rules" (avizrayhu) of those mitzvot. (The specific example there is not relevant to us.)

There are two relevant halachic principles here: the first is ביטול ברוב, that things can be ignored if they are some type of minority (without going into the details). The second is a restriction on this known as טעם כעיקר - the taste of a thing is like the thing itself, and if it can be tasted it is not negligible. Do either of these apply to gentiles?

R' Ya'acov Ariel discusses it here, and mentions that the Hatam Sofer (YD 94) says that the law of רוב does not apply to Bnei Noach, and טעם כעיקר does, so the taste of aiver min hachai should be forbidden to them. The Beit Yitzchak (OC 29:7) disagrees, saying that טעם alone being forbidden only applies to Jews (Psachim 44b), so the pots are not forbidden. The Yad Elazar agrees with the Hatam Sofer.