Using one or the other changes the meaning of the sentence.
・"Do you see something in the sauce?" This means that the one asking has a suspicion that there's something in the sauce; perhaps the one that is being asked is looking closely at the bowl and is squinting.
・"Do you see anything in the sauce?" This means the the one asking is just requesting an inspection, in case there is something.
"Something" is a much more specific word than "anything."
It's not optional in any but the most informal speech. If you're going to omit the "Do", you might as well contract "going to" to "gonna" and "are not" to "ain't".
Making a statement and using voice inflection (or a question mark) to turn it into a question if that statement is true is perfectly fine in Spanish. It is not fine in either Hebrew or English, but whereas it is only somewhat slangy in Hebrew (don't write it in your term paper), it's very much inferior language in English.
See the answers this guy is getting: https://forum.wordreference.com/threads/omitting-do-in-a-question.539970/
Do is an auxiliary verb. The inclusion or exclusion of the auxiliary verb does not change the meaning of the sentence, it simply adds emphasis. Whether or not this is acceptable in formal speech is much more subjective because there is no governing body of the English language like there is for Hebrew. I do think that adding "do" is better but I disagree that it is necessary. Interestingly enough, I knew that it could be omitted as a native speaker instinctively but I had to look it up to give you the reason why.
Respectfully, are you a native English speaker?
In addition to providing do-support in questions and negated clauses as described above, the auxiliary verb do can also be used in clauses that do not require do-support. In such cases, do-support may appear for pragmatic reasons.
"You drove here?" instead of "Did you drive here?"
"He wants to come?" instead of "Does he want to come?"
"Mario talked to his boss?" instead of "Did Mario talk to his boss?"
Sure, these questions are all grammatically correct, but they're a type of echo question and they might not be what was intended.
I am not a native English speaker, although I did (for emphasis) live in the US for several years. Both the links that you sent support my position.
"The presence of an auxiliary (or copular) verb allows subject–auxiliary inversion to take place, as is required in most interrogative sentences in English.". Note the word required. The section about emphasis is for statements, not questions.
From shmoop.com you included the relevant quote yourself. Without adding the auxiliary verb this is an echo question, not an interrogative and that "might not be what was intended". Definitely not what was intended here.
I agree with Khthbnsrl. The Hebrew sentence does not start with האם. Much like other learners, I translate the prompt one word at a time, and by the time I reach the end of the sentence and discover the question point, it seems counter-intuitive to go back just to add a "do", especially since the sentence makes perfect sentence in actual real-life English, regardless of what grammar books say.
What's more, I know for a fact that the form without the do-support is acceptable as a solution to some of the other sentences in this course that are also Yes/No questions.
"Informal" does not mean "wrong". If you're eating with somebody (and hence asking them about the sauce), chances are you two are familiar enough for formal language to start to sound stuffy. A good language course teaches you a range of registers for the same language, and teaches you how to decide which is appropriate.
Anyway, I reported it.