Ik heb er zin in: I feel like having/doing/eating/... it. Depending on context other translations could feel more natural, e.g. "Vanavond ga ik feesten; ik heb er zin in." Tonight I'm going partying, I'm looking forward to it.
Ik lust het: I like it, or, depending on context, I don't dislike it. "Ik lust spinazie." I like spinach.
Ik vind het lekker: literally "I find it tasty", so pretty much the same as "ik lust het" but a bit stronger.
Ik hou er van: like you said: I love it. Much stronger than the previous sentences.
First of I like it and ik lust het do not mean exactly the same though there is an overlap. So without the explanation of the difference I don't think they should have chosen this sentence.
ik lust het niet ís usually used when you find something so disgusting you really don't want (and sometimes physically cant) eat it. So it goes beyond not being you favourite. It is something not edible in your personal opinion. You wouldn't eat it even if you got payed.
There are a lot of things I find ok or fine like bread. Ik lust het but wouldn't say ik vind het lekker. I won't eat it simply for the pleasure or enjoyment. Or looking forward to when I can eat it. Like people do with their favorite dish or something like chocolate.
To go back to the specific phrases in your question:
Ik heb er zin in=I feel likeit/ looking forward to it/ have a craving for it.
Ik lust het= I am okay with eating it.
Ik vind het lekker= I like it/(I think) it tastes good.
Ik hou ervan= I love it. (Though the Dutch is slightly less strong than the English love. More like I enjoy it. Not I am absolutely mad about it (not usually anyway)
'Hutspot' is potatoes, carrots and onions (I seriously can't eat it, I find it disgusting). 'Stamppot' is potatoes with certain vegetables and sometimes meat. Technically, 'hutspot' is a 'stamppot' (but not the other way around)! I see 'hutspot' really as a dish. 'Stamppot' is more of a traditional Dutch cooking method.
That's right, "stamppot" is more like a family of dishes. A classic one is "stamppot boerenkool", consisting of mashed potatoes and green kale that was endlessly boiled. Usually it is eaten with smoked sausage ("rookworst"), which is really the only tasty part of the dish. The trick is to get at least one piece of sausage with every bite!
Also, "stamppot" is pretty much only eaten in the winter.
https://nl.wikipedia.org/wiki/Hutspot According to wikipedia stamppot is a group of dishes of which hutspot is one. Meat can be added on the plate, but it is not included in the hutspot. But the dutch are not so strict, you can make your own variations. I think there is a difference in the way it is prepared. Stamppot is made by using a "stamper" to smash the food. A hutspot is prepared by cooking the food till it falls apart by itself (huts, or hutselen is an old dutch word, hardly used anymore with the meaning of mixing. So the food of the hutspot is cooked till it is almost soup and than mixed using a large spoon. If you are looking for ingredients try this one: http://www.smulweb.nl/recepten?query=klapstuk
No, the dutch word "lust", is much weaker than the English word" lust". They have the same origin but developed in opposite directions. In english one would ask something like: Are you eating apples at all? And the answer could be: i don't like them. In dutch: Ik lust ze niet.
Lust for food is when you are not against eating it (ik lust het wel/niet) Or in ik lust wel wat i feel like/I could use something.
Besides for food it is also used for sexual lust.
Keep in mind that in Belgium sometimes they use different words or the same words differently, eventhough it is technicall dutch. I think this is one of those cases (instead of lust for food I believe they use goesting (cognate of gusto from Latin gustus). And I think there are some other differences. Perfectly fine to understand for me but not enough knowledge to reproduce it correctly.)