You shouldn’t have any issues travelling with both passports. If the check-in desk questions you ask for a supervisor who should know what they’re doing.
That’s the resultant PDF of doing a filing online. You asked what the form looked like. The form is for when you are doing a filing in-person at immigration.
That’s gonna depend entirely on the office they’re using. Some offices require a new TM30 when returning from abroad or even if you’ve stayed a night in a hotel in country and returned.
You'll rarely be asked for an onward ticket at immigration, but it's possible. Usually, the issue lies with the airline, as some insist on an onward ticket within the allowed entry scheme days, while others don't seem to care.