I would recommend to you, in future, that whenever you get an extension of stay, get a multi-re-entry on that same day. This is what I do, so I never forget.
No limit, but someone having a bad day will apply one. Avoid female Immigration Officers. In my experience, they are most likely to give you problems. Not being sexist, just factual, and based on experience. If you plan to stay longer term, with more visits, get a DTV or similar.
Ah right. Under considerstion for extensions are definitely fine to leave on and return. I did this last month, with a re-entry, with no issues. In Pattaya, a home visit is required. Not sure on other offices.
You say visa application. Do you mean NON O visa, or extension of stay? Marriage or retirement, and which office? You can leave during both, with a re-entey permit, but you will have to be very up front with immigration. If it is a marriage visa or extension, some offices want to visit your home. Return to the office on the review date and you will be fine.
You think wrong. NZ citizens can definitely apply for a NON O for Thailand, and I would recommend that this is by far the best option in this situation.