You said you asked for an 85 day visa? All tourist visas are 60 days. Just curious, did you think visas are granted for a custom number of days depending on what you request?
Most major airlines have a fully refundable full price fare that you normally have to buy directly from the airline website. It's normally much more expensive than the normal nonrefundable fare. Of course the funds have to be available on your credit card for the initial purchase.
The assumption I had was being in that lane means you have money either to fly business class or to have an elite visa or at least bought a concierge service, so you're viewed as more a "desirable" tourist they want to come spend money in Thailand. But someone sent me a private message that the one time they got hassled was when using fast lane. His theory is the immigration officers don't have to deal with a mad rush of people and so have more time to peruse your entry history and ask you more questions. So maybe it isn't that great an idea.
It doesn't seem Dominican Republic is on the list of countries that are either Visa Exempt or Visa on Arrival which means you cannot enter Thailand unless you get a Visa in advance from a Thai consulate or embassy, according to the Wikipedia list. Once you get either a single entry or multi-entry tourist visa at a consulate or embassy, you can stay 60 days, but can extend it at the immigration office for either 7 or 30 more days for 1900 baht (depending on what country you are from). I can't find whether Dominican Republic is allowed a 7 day or 30 day extension.
I absolutely can confirm from personal experience that immigration just told me to carry both the old and new passports together and that they don't transfer visa stickers from one passport to the other. People always get confused as Visa Exempt stamps must be transferred to new passports but not actual visas.
The ticket requirement just means you need to print the email confirmation (or show physical ticket) that has the actual long ticket number from the airline, which proves the ticket has been paid for. What they don't accept is the 6 digit alphanumeric confirmation number issued by the airline (the one you use to check in for your flight or make flight changes) since that doesn't prove the ticket was ever paid for or issued. The 6 digit confirmation number could just mean you have a ticket on hold that will be canceled because you never paid for it. For example, Bangkok Airways will send me an email with the 6 digit confirmation number when I call them to make a reservation that I want to pay for in person at the ticket office or at 7-Eleven, but they don't send me an email with the actual e-ticket number on it until I make the payment and the ticket is issued.
Assuming you bought your ticket online, once a ticket is paid online and the ticket has been issued, the airline or booking website such as Expedia, sends a final version of your itinerary that includes the ticket number. That's why often when you buy a ticket online, you first get an email confirmation that only has the 6 digit confirmation number before the ticket is issued, then another email a few minutes or hours later that will include the full long ticket number along with the 6 digit confirmation number. The reason they still include the 6 digit confirmation number is that is what you use to check in to your flight either online or at an airport kiosk, but the super long ticket number is the actual proof the airline issued a ticket to you. That's the email you want to print out.
If you don't get the visa in advance, you run a small risk of immigration asking to see your return ticket and denying you since technically you are required to prove you are exiting the country before your visa exempt period is finished.