Hello, First of all, I want to point out two things: (1) I have spent several hours over the past week or so looking for the answers to my questions online and in style manuals, and (2) I have not had any formal training in proper English in about 5 years. I am editing a piece of (my own) technical, academic writing, and I have run into some punctuation problems that don't seem to be covered in any resource that I have tried. If there is another area of this forum for technical writing, then hopefully a moderator will move this post there for me. Also, I did try the search function with "compound conditional" and "compound protasis" first. For the first problem, I don't know if a compound clause in a conditional statement needs a comma in it if it normally would need one as a stand-alone sentence. Since the writing is technical, I will present two made up examples: or In the first example, the first clause would normally need a comma after the word car. I have not been able to find a resource that presents any kind of rule for that. The one thing I did find that was even remotely related was that commas are there primarily for clarification, so if adding a comma makes the separations that achieve the desired emphasis, then put it there, but if adding a comma introduces any confusion, then don't. That's sage advice, but I'm hoping that there's a more specific rule. Additionally, in some of the sentences, I think that using a comma would make the sentence confusing, whereas others would be fine with a comma. I want to be consistent. Obviously, reforming the sentence may avoid the problem, but I'm trying to convey very technical ideas, and I'm trying to do so in the clearest way possible, not necessarily with the simplest grammar. I think the compound conditionals I'm using convey the right meaning in a clear way, but I want to use correct punctuation. The second problem is with a sentence from the acknowledgments section, so I will just give the real sentence: Here, I don't know if there should be a comma after "interest." When spoken, there should be a pause, but I've read that that is not a very good guide of where to put commas. Any help at all is greatly appreciated.
The problem with "looking up rules" is that you need to know what you're looking for. In your first set of examples, you are dealing with subordinate clauses and main clauses. In the first sentence, you don't need a comma after "car" because the two thoughts are linked by the conjunction "and". The comma after "store" is necessary because it separates the subordinate clause from the main clause. You do not need "then" after the comma in either sentence. My "go to" reference book for most grammar and usage questions such as yours is The Little, Brown Handbook. Your second example from the acknowledgments section needs to be completely re-written. It's too awkward and cumbersome to fix by merely adding a comma, although a comma is necessary after "interest" as written. I don't want to re-write it for you but I can give you an example of how you could write it more clearly: It was his course on elliptic curve cryptography that initially sparked my interest. Our many discussions about background material, as well as his guidance in working out the details of the proof and his advice on writing style, have been immeasurably helpful.
I would think of it this way, being at the store is dependent on both getting in the car and driving. Therefore, the comma goes before 'then' (although I agree with James that 'then' isn't really necessary anyway.)