You certainly can use an article with the other words. Here's a breakfast of tortillas, here's a filling lunch, here's I once hosted a dinner. The use of the article here is more or less the same as it is anywhere else: it indicates a specific example of something as opposed to the general concept or phenomenon.
A lot of food terms are non-count nouns or can be used in a non-count sense, for example coffee:
It's a matter of learning which words are used in a mass noun sense and which aren't. For example, breakfast, lunch, dinner, supper, brunch, coffee, and ice cream are usually mass nouns because they refer to general phenomena or materials, but it's also perfectly acceptable to refer to (for example) a brunch if you're referring to a specific one.
Sandwich is not a general phenomenon or material, but a discrete object, so it's always "I had a sandwich", never "I had sandwich." Likewise, meal is not a phenomenon or a material, but a specific thing, so it's always a meal (when it means "a specific instance of having food"...there's also a definition of meal that means "ground-up seeds", and that one is a mass noun.)
Drink is a little bit of an odd case, because it's normally a count noun if it refers to "specific things to drink" (let's have a drink or let's have drinks) but a mass noun if you mean "things to drink in general" or "alcohol" ("attitudes relating to food and drink").
Best Answer
"I have a/an X" does not necessarily mean that I have exactly one X, it just means that I have one or more.
Suppose someone was looking for a ride home, and he asked, "Do you have a car?" If you own two cars, you wouldn't say, "No". You probably wouldn't even find it necessary to say, "I have two cars". You'd just say "Yes". (Well, unless you're looking for an excuse to not give him a ride.)
Suppose your local school announced they were having a "father/daughter dance", and said, "This is open to any man who has a daughter in this school." If you have two daughters, would you conclude that you were not welcome? Almost certainly not.
Or to take it a step further, if someone asked, "Do you have a daughter?", and in fact you have one daughter and one son, would you say, "No, I don't?" Probably not. Or if someone asked, "Do you own a cell phone?", would you say "no" because you own a cell phone and you own a laptop computer and you own a car and you own six pairs of underwear, etc? Normally, asking if you "have X" doesn't imply "and nothing else". If you want to specify "and nothing else", you normally need to add some words, like "only" or "just one". Like if someone asked me, "Do you have only one daughter?", I would answer, "No, I have two." I might also say that I have two sons as well, if the context of the question implied that the person was asking if I had only daughters.
All that said, there may be contexts where it would be understood to mean exactly one. I can't think of one, but I can think of a somewhat similar example. Suppose someone said, "In this country it is illegal for anyone under 18 to buy alcohol." If in fact the law said it is illegal for anyone under 21 to buy alcohol, there's a sense in which the statement is technically accurate: Yes, it is illegal for anyone under 18 to buy alcohol. But it is also illegal for anyone between 18 and 21 to buy alcohol. But as worded the sentence is very misleading. It implies that anyone over 18 can buy alcohol, without actually saying that.
I suppose if someone said, "We are holding a conference for parents of girls being raised without any brother or sisters, only children who are girls. You sir, do you have a daughter?" Clearly then he means exactly one, but this example is highly contrived.