I am not really familiar with this particular system/form but here are a few suggestions:
- Depending how you look at it, your H1B visa was issued by the US or by a specific consulate (if I am not mistaken, it's called “Issuing Post” in official US parlance). Writing “US consulate in XXX” would in any case unambiguously provide all the information the German consulate could possibly wish.
- Your passport is generally issued by your home country. So, for a regular passport, writing “India” or possibly “XXX office in [Name of your city] (India)” (or whatever the relevant agency is called in India) or, if you live abroad, “Consulate of India in XXX” should be just fine.
At the end of the day, many Indian citizens will have a passport issued in India and by India but there is a distinction between “citizenship“, “issued in” and “issued by” because of two special cases: People residing abroad and people who can't get a regular passport.
For example, I don't live in my country of origin so my passport was issued by my country (and, more specifically, by one of my country's consulates) but in another country (and, more specifically, in the city where that consulate is located).
For the second case, refugees often cannot ask their country of origin for a passport (after all, they have this status because they are persecuted in this country) and stateless people have no state to turn to to get a passport. So what these people have (when they are lucky) are various types of passport-like travel documents (1951 or 1954 Convention travel document or, if they live in a country that is not party to one or both of these conventions, some sort of ad hoc refugee travel document, re-entry permit, etc.) In all the cases, the travel document is issued by and in a country that's not the person's country of citizenship.