The translations are correct, but the mythological sources that comes closest to discuss what a human needs to be a human uses other words, with different connotations, as well as totally different concepts.
First, let me note that the above seem very speculative: we do not have the sources to really discuss how the Old Norse saw the self. The purely mythological material is pretty bare-boned. We can probably do a bit more if we go to medieval Icelanders and use the saga literature, but then we likely have some Christian influence to contend with.
From a mythology standpoint, the most relevant part is when Odin and two companions create the first humans, Ask and Embla. They are given gifts to make them fully alive. This is told in Völuspá, verse 18, and in Gylfaginning, chapter IX. I will quote the relevant passages in Old Norse:
Önd þau né áttu,
óð þau né höfðu,
lá né læti
né litu góða;
önd gaf Óðinn,
óð gaf Hænir,
lá gaf Lóðurr
ok litu góða.
- Völuspá, Edited by Guðni Jónsson
Gaf inn fyrsti önd ok líf, annarr vit ok hræring, þriði ásjónu, mál ok heyrn ok sjón, gáfu þeim klæði ok nöfn.
Gylfaginning, Edited by Guðni Jónsson
The exact meaning of these passages has been debated, and there is no exact translations. I will try to cover the gifts as noted in Völuspá, from as many translations as I can find:
önd is a complex noun, and can mean spirit, breath, soul, mind or life (the word is still in use in northern Germanic languages, and keeps most of these meanings. It is particularly in use in Christian contexts for the Holy Spirit). This seems to be translated as "spirit" or "soul".
höfdu (I'm not sure what the unconjugated word would be). This differs across translations: "sense", "judgement" or "force, power, energy".
lá. Another tricky one. Outside of poetry, the meaning seems to be "hair", but two of my translations have "blood", the third something like "fluid of life", while the last have "heat".
laeti. This can mean "sound (from human or animal)", "manners, conduct", "good will". My translations into Swedish have gone with "sound" or "voice", while the English have "motion".
litu góða. lit means something like "look". góða is "good". This seem to translated to "good skin", "lively hue", "lively color".
As for Gylfaginning, we have already covered önd, while líf is "life", vit is "knowledge, wit", ásjón is "shape, looks", mál is "speech", heyrn is "hearing" and sjón "sight". The last two gifts are "clothes" and "names".
So, if we sum this up, humans would need a spirit or soul, sense or wit, looks, and senses.
If we compare with the list in the question, we can at find somewhat decent fits for "body" and "mind", but not for the other two. A fylgia is properly a sort of spirit companion; it can both be connected to the ætt, in which case it can take the form of a person and appear in omens, or be a sort of personal alter ego in animal form. Hamingja is indeed a form of "luck", and can be personified by a woman. It can also be a sort of soul that can be transferred from one person to another within the ætt.
I've used the online Old Norse-Danish dictionary from the University of Copenhagen for the basic meanings of words.
For Völuspá, I've consulted the translations done by Erik BrRate and Lars Lönnroth into Swedish, and Benjamin Thorpe and Henry Adams Bellows into English, as found in Wikipedia.
For Gylfaginning, I've used the Swedish translation of Karl G. Johansson and Mats Malm.
For Fylgia, see Gro Steinsland, Fornnordisk religion.
For Hamingja, see Britt-Mari Näsström, Nordiska gudinnor.