I don't believe kelp is a countable noun, so your first and second sentences are correct.
Your third and fourth sentences are not correct, though. You'd simply say, "I ate kelp," or "I ate some kelp."
Kelp is an uncountable noun.
How can we use kelp?
I ate a kelp.
I ate two kelps.
(Are the expressions correct? How can we count 'kelp'?))
3 answers
Here's a bit more information. Notice how the word is used in here:
http://en.wikipedia.org/wiki/Kelp
http://en.wikipedia.org/wiki/Kelp
http://esl.about.com/od/grammarforbeginners/a/g_cucount.htm