it was detailed In the press release last week. Visiting Thailand, returning home then coming back to Thailand several months later is consistent with being a tourist/visitor.
Yeah, there are a couple of approvals via Tokyo which should be in the threads. Note Tokyo is very strict with approval and often issues 6 month TV Instead of the DTV. Fukuoka and Osaka are 'friendlier'. Make good use of Tokyo's free pre application service and focus on showing long term need to have the 5 year visa.
Showing income deposits is a requirement for many embassies to get approval. Requests for pay slips, and payment of services are common as many posts show,
It is not a problem. You can come and go as you please, the DTV is a multi entry visa. You could mention in a cover letter your return home in April and then returning to Thailand to restart your training
Should not have any probs, as you are going back to your hometown. The rules are focused on the border hoppers who are staying long term in Thailand without a visa to cover their stay.