what I understood from the table was that the reason it has to be "viele" is that "Kartoffeln" are feminine.
No -- it's because Kartoffeln is plural. It's not feminine.
The singular Kartoffel would be feminine, but the plural is plural.
I don't see what a preceding article would have to do with it.
That's what selects between strong, weak, and mixed inflection.
"Strong inflection is used: [...] when no article is used."
So since there is no article, you look up the "strong inflection table" (rather than the weak or mixed one), and then look for plural accusative, and find the ending -e.
In this case, the "viele" is not because potato is feminine, but because it is plural. Use Google Translate, and type in "I have many potatoes" for translation into German. Then change the object to a plural masculine noun, like dogs, hats, apples, and you'll see the "viele" from potatoes stays "viele" for masculine nouns as well. Don't confuse yourself with the strong, weak etc inflections yet. You'll see "vielen" when an article is put before "viel." It's "viele Kartoffeln" but "die vielen Kartoffeln," and "viele Meere" but "die vielen Meere."
What other forms of word viel/viele are there? We have "viel" for much, and is it the same word in all positions (nom., acc. Dat.) And all genders?
"Viele" for many, but ending could change based on gender or case. If so, how we write it with different genders and in different cases?
And "vielen" which is many as well, but in case there is article before it or in Dat. Case?
I think "a lot of" and "several" mean different things. "A lot" is more ambiguous than "several". It's just making the statement that lots of potatoes are being eaten. not anything more exact, because it doesn't need further elaboration.
I am sorry if I am wrong, good luck! :]
It may be "standard" for some, but it is a misspelling, and therefore not a correct answer. "A" is an article, and writing "alot" for "a lot" would be the same as writing "'acat" for "acat" would be.
Simple Definition of lot
: a small piece of land that is or could be used for buiding something or for some other purpose
: a small object used to choose the person who will do or receive something
So you see "a lot" refers to a known amount of something. In english we refer to a piece within an auction as a lot because it is a piece of the whole.