No, that isn't true.
Vietnam doesn't operate a true "Visa on Arrival" system. In additional, all visas for Vietnam have a fee. Some nationalities can enter without a visa, paying nothing and being allowed to remain for 15 days, but neither of your nationalities s are included in that list. Your options for entering Vietnam are:
Apply for a visa in advance ...
A. Effective December 30, 2008, Maltese citizens are eligible to
travel to the U.S. without a visa under the Visa Waiver Program if the
following conditions are met:
The visit is less than 90 days
The visit is for tourism or business
The traveler holds a valid biometric passport
The traveler registers for and ...
Since the flights are with different airlines and I would need to collect luggage
Note that this only applies if it's in separate bookings. If it was a single booking, it'll be automatically checked through.
As per the other answer, to enter Turkey you can get an e-visa (on the Website or at the kiosks), using either your passport or ID card.
Since the flights are with different airlines and I would need to collect luggage do I need to go through passport control to connect to the emirates flight?
Yes, to collect baggage you must go through passport control first.
Also do I need a visa for transit?
Yes, baggage collection is a landside activity hence you will be entering Turkey and will ...