If you have 3 months or more left on the visa shouldnt be an issue. Less than that might be risky. Some people have had to wait upwards of two months for the dtv to be approved. Just something to consider.
Under the assumption that all your papers are in order, if there is enough money in the accounts 500k + 500k thb ( another mil for the kids) and then some, you and your husband should apply independently first, because there's no such thing as a 'joint application'. It is okay if the bank accounts are joint the key factor is that the applicant has acess to these funds.
What you can do is make one account for the evisa portal and submit both independent applications through the same log in account.
Once that is done and approved, hopefully, you can apply for the kids as dependents. Or just one of you can apply first and the others all apply as dependants, this might cut down some of the paper work.
Alternatively if you're actually planning a long term move you should consider getting the kids on ed visas maybe and then you apply as their gaurdian.
it's not considered a "long term visa" legally, so it would be down to the discretion of the japanese embassy. No one else can answer this for you. Try emailing them again with the exact question of if they consider dtv as a long term visa. Maybe add a pic of your entry exit stamp.
No worries about nationality, they just want to see sound finances and if you can sustain yourself. I believe some iraqi and syrian nationals have posted on this group before about approval, try using the search function.
Just highlight the exact transaction relating to each payslip and write cover letter explaining the prevalent exchange rate and whatever flat rate fees your bank charges for receiving.
It's a request to check authenticity, because they didnt understand whatever documents you've sent, not a math test or tax audit.
The three month rule change seems to be fairly new, based on posts in this group, I would recommend rectifying with the issuing consulate by phone or email rather than rely on fb comments.