No, you can't. You do it once. The second time you're going in person for an extension and why would anyone report on day 360 when they have to leave the country anyway?
You can, in practice, only do ONE online report for a 360 day DTV stay, which is on day 270.
Anonymous participant Calling is a waste of time. No guarantees of what language the person picking up the call will speak, and they certainly won't forward your call to the individual who reviewed your application. It's email or nothing. A phone call is a pretty confrontational method of communication for a matter like this; if they don't respond to your emails then there's nothing you can do. You move on.
I can assure you an American embassy or consulate will NOT entertain phone calls from applicants asking why they were rejected for a visa. Therefore, I see no reason why a Thai embassy or consulate should be any different.
Ho Chi Minh communicated with me via email when I contacted them. Most embassies don't respond to phone calls. Calling an embassy or consulate to ask them why they rejected you sounds like an odd thing to do. Requesting clarification via email makes sense, but if they don't respond, there's nothing you can do.
You need to depart the country BUT I wouldn't do a same day border run to activate the visa, as it will be a bit suspicious. You spend a few days outside of Thailand, THEN return with the DTV. Besides, I don't see the urgency of returning to Thailand anyway. It's always nice to have a vacation and see something different for a few days, especially if you're a tourist or even a DTV holder.
No, the second report would be done in person as you would be due for an extension. On day 270, you could do an online report, but that could only be done once a year (as in, online once a year), because by the 360 day mark you have to leave the country and the clock resets.
But online can ONLY be done once on each entry. If you get an in country extension, you effectively report in person at the 180 day mark, as you'll need to extend your stay then. For the 270 day report, that can be done online. At the 360 day mark, you need to depart either way, so no point in filing a report then.