Do the grammars of sign languages accommodate speech acts that are more complex that e.g. declarative or interrogative statements in the same way that spoken/written languages do?
For example, are the following expressible in sign languages such as ASL?
As sign languages are complete human languages I’m puzzled as to why you think they would be deficient in such a manner. They are as complete and as expressive as any spoken language, although, because their grammar and syntax vary (as is true of all languages) literal translations would sound odd to an English speaker.
You’ve got two distinct parameters: form and function.
Form is what we call “grammar rules.” These vary from language to language. For example, English uses Subject-Verb-Object but Korean and Japanese use Subject-Object-Verb.
Function is communicating meaning. In the case of reported speech, if nobody followed the general conventions, we’d all be hopelessly confused.
Between any two random languages, form differs, sometimes on major points, often on minor points. British English and American English, for example, has many differences in form:
American: I will go out on the weekend.
British: I will go out on weekend.
Americans would mark the British use of “on weekend” instead of “on the weekend” as an error.
However, in terms of function, all languages share the same functions. For example, all languages have ways of expressing refusals, and in all languages, the longer it is the more polite is it perceived:
Question: Can I borrow your car?
Answers:
No. (Refusal)
Sorry, but no. (Apology + Refusal)
I’d love to let you borrow my car, but not today. (Affirmation + Refusal)
I’d let you borrow my car but then I’d be stuck, so sorry, but I can’t. (Affirmation + Excuse + Apology + Refusal)
Therefore, the function of say reported speech exists in all languages, but the form will vary widely.
I once “heard” a talk by a deaf linguist whose thesis was there was no effective difference between sign languages and spoken languages. They had the same kind of complicated rules and means of expression. (There were interpreters in both directions, so I guess I did hear it.)
Some Americans have some very odd notions about British English. As a British person I can assure you that “I will go out on weekend” is erroneous in British English too.
In certain British dialects, such as Yorkshire, one might say “I will go out on t’ weekend,” partially suppressing the “the,” but if it lost the “t’” altogether it would certainly be considered ungrammatical.
“British English and American English, for example, has many differences in form” is erroneous too. 
True, but there are examples of British English dropping an article where American English would retain it. Such as “on holiday” vs “on a holiday” or “in hospital” vs “in the hospital”.
But these mean different things, don’t they? “On holiday” in BrE corresponds to “on vacation” in AmE (no article required in either case). If using “holiday” in the American sense of a non-working day or celebration day, British speakers would indeed say “on a holiday”.
I think the British equivalent of “on the weekend” is “at the weekend” but I’m not 100% sure.
This is one of the reasons why you hear the phrase Registered Interpreter for the Deaf, rather than translator. Effective transfer of information between any two languages always requires some amount of interpretation (such as when idioms come into play) but much, much more so where sign language is concerned.
Translation gets the key words from one language to another, but interpretation gets your meaning and inflection across.
Sign language interpreters are called interpreters rather than translators because they are interpreters rather than translators. That is, interpretation is a real time thing, whereas translators work with non real time language uses. It’s not a sign language versus spoken language thing. Someone watching a video of ASL and producing English subtitles for it would be translating, not interpreting.
Back before I was a RID I was always corrected by other RIDs for using the term “translator”, and told that translators work between two spoken languages. Interpreters work between a spoken language and some form of expression such as stories told through non-traditional means such as dance. Personally I think that sign language is just as well-defined as any spoken language, but I will admit to not being an expert on such matters. Maybe I have been conditioned to see a biased difference between the two ideas.
A quick peek at the UN web site shows that they list their job openings as both translators and interpreters. I’ll also point out that ASL - which typically does not contain a lot of synonyms, has two different signs for interpret and translate.
Good point. Surely among the Doper community we have at least one such interpreter? If one of you is reading this, would you kindly describe how you’d interpret the examples from the OP using ASL? I, for one, am curious as to how the grammar and/or syntax differs both from spoken English and between the three examples in ASL*.
*Also, I welcome our new robot overlords.
Well since I’ve already identified myself as a RID, I’ll chime right back in. But be careful not to expect word-for-word translation with sign language. That’s known as Signed English and is not how casual, er… “speakers” communicate. Signed English is used where verbatim translation is required and when teaching school children proper grammar and sentence structure for reading & writing. That’s why ASL interpretation is more of an art form that translation between two spoken languages.
The time of day and exact situation might call for some slight modifications, but here they are. The actual signed parts are in quotes:
[Establish a location for X and point to it to identify the subject, or use subject’s name] “told me” + “eat” [with negative inflection via facial expression or shaking of head] + “now” [if it’s lunch time] or “lunch”.
“If” + “meeting” + “finish” + “soon” or “fast” + “then” + “eat” or “lunch”.
“If” + “meeting” + “finish” + “early” + “then” + “eat” or “lunch” + “but” + “happen” [happen signed with negative inflection via facial expression or shaking of head].
Somebody else might sign that a little differently while getting the same ideas across. That’s what I identify as the interpretive part.
Thanks! That’s exactly what I was looking for.
While this topic is here, I have a question. There was a deaf girl with an interpreter in my Earth Science class. Now the professor was very sarcastic. Does ASL have special signs to say “This is sarcasm”?
FD: I am not an ASL user. However. How do you know your prof was being sarcastic? Usually you can tell not because of special words he used, but by his facial expression, tone, etc., and ASL users have those things too.
True. And in British English "in hospital and “in the hospital” are both acceptable, but have subtly different meanings? Does American English lack this distinction?
I agree that “at the weekend” might be more common in Britain than “on the weekend,” but I think teh latter would be acceptable (whereas “on weekend” certainly would not.)
I don’t think so. I’ve never heard an American say “in hospital”, and I am completely unaware of these “subtly different meanings” you allude to. What are they?
“In hospital” refers to the state of being under medical care in said building.
“In the hospital” refers to physical location - if you’re visiting a friend in hospital, you yourself are in the hospital.
It’s like “at school” versus “at the school”: if you’re aged 4 to 16 then you’re probably “at school”, regardless of where you happen to be at that moment. But during the holidays, you’re unlikely to be at the school. 
Oh, I see. If we have the distinction at all (and for the most part we don’t, I think) it would be as follows:
In the hospital: receiving treatment
At the hospital: visiting someone in the hospital or working there.
That’s because a translator works on delayed time (most usually in a written medium), while an interpreter works in real time on spoken (or signed) medium. The UN needs both functions, and they are covered by different people.
When someone hands me a patent that they need to be able to read, they’re asking me to translate. When they drag a truck driver into the lab asking me to translate a series of instructions in real time from the warehouse guy to the trucker, and the trucker’s response back, they’re asking me to interpret. If the warehouse guy is American and the trucker is Italian, half the talking I will do with the trucker is gestual…