Haigh, Bama.
These pronouns are not quite duplicates of each other, even though they mean the same thing.
The use of "sé" is for subjective mode, that is, when used in the subject of a sentence.
The use of "é" is for objective mode, or when it is the direct object or refers to the direct object in a sentence.
Technically, you have mistranslated your first example sentence. "Cuir sé ar an mbord" (or an tábla) actually means "He puts on the table." What is put is not specified in that sentence. Part of your confusion might be from the fact that the subject in the sentence "Put it on the table" is implied; "You put it on the table." To say "Put it on the table" in a directive fashion, you would use the imperative form, but it would be "Cuir ar an mbord é!" Put it on the table! In this case, the "it" is the object in the sentence (the thing being put) so it should be "é". The verb form should also be adjusted for the third person, which would be "Cuireann sé ar an mbord é" He puts it on the table. "Cuir sé ar an tábla" might be understood, but is technically not correct grammar, as I understand it.
In the question, Cad é mar atá tú?" How is it with you? the structure of the sentence as a question makes you the subject and it the object, so the rule of using é is properly employed there. I personally prefer the simpler, Conas atá tú? However, each dialect has their preference for how to say that.
You will also find é and í frequently used with the copula: Is maith liom é, "I like it." Literally, "It is good with me." My understanding is that é or í are always used with the copula, and should be consistent with whatever "it" is; if a male noun, then use é, and if female use í. There is another use concerning the copula where the pronoun seems to be doubled, but it is a way of identifying something as the only one of something: Is é an bunreacht é; "It is the constitution." Although the "é" seems to be repeated or dedundant, it is actually saying, "It is the constitution, the only constitution, there is no other constitution."
I know this can be a little confusing, and you have to really think about what in your sentence is the subject and the object to use the correct pronouns. But with practice, that will start to come around.
I do not remember how I explained this last time, but I am pretty sure this is correct. It may be possible that "Cuir é ar an mbord" may be correct as well, but even I am still sorting out some of the details....
Dale D