Should there be a liaison between des and haricots when spoken?
No, the "s" on "des" is not pronounced here.
There are two kind of "h" and one of them are silent all the times. The "h" in haricots is of that kind.
I said " I eat some green beans", not accepted
No, I think that "some green beans" should be accepted. Try reporting it next time
I think you can say "some" only where there is a "du" or a "de la" and not "des".
Take a look here: https://www.thoughtco.com/du-de-la-des-1368977
"Des" (here) is the plural of "un". There is no counterpart in English for this word. Some people feel it necessary to use "some" in an effort to translate each and every word. In reality, this sense of "some" is almost always ignored in English.
How do you tell when it is 'ate,' 'eating,' 'is/am eating,' and so on? Mange, mangent, mangez.
In French 'I eat' and 'I am eating' is said in one way: 'je mange'. 'Ate' is past tense, so it would be, 'je mangeais' (imparfait) or 'j'ai mangé' (passé composé).
Additionally, "mange" is the present tense conjugation of manger for "je" and "il/elle/on" (first and third person singular). "Mangent" is for "ils/elles" and "mangez" is for "vous"
"I eat green beans" not accepted
What have green beans got to do with clothing - which is the title of this section.
in English they are called French beans