If your friend is a passport holder of one off the 93 countries that are allowed visa exempt entry, she will get a 60 day visa exempt stamp which is free then during this time she can apply for a 30 day extension at her local immigration office which will cost her 1,900 baht, giving her a total of 90 days inside of Thailand.
Highly unlikely immigration at the airport will question her, if anything the airline she is using might question her upon check in.
It is not a visa, the proposed ETA is a electronic travel authorization, and it is only a proposal at this stage, so don’t be too worried, a lot of countries have a ETA in place.
Most immigration offices will give you a hand out which outlines the visa requirements for that particular office. Go there and ask them, it is a fairly easy process to do yourself, if you are organized and meet all of the requirements.
You don’t say your age, and what amount of coverage you require, that would help narrow it down. But try looking at AXA or Pacific Cross, you can search all this yourself.