You're right about the Laotian influence. But generally, Isaan people still consider themselves proud Thais because I suspect they think being Thais is a step up from being Laotian.
1. There has never been an issue with Isaan's nationality as Thais, carrying Thai identity cards and Thai passports, the reasons are obvious, economically both countries are a world of difference. And therefore yes Thais are generally perceived "a step up" from Laos.
2. The word "Isaan" is being used on them only in the early 20th century in a program known as Thaification to simply make them more Thai and this is emphasised in 1950s onwards due to communism.
3. Say what one like Isaan people today use the words on themselves Lao more so ethnically than nationally so the saying Ahan (food) Lao, Pasar (language) Lao, Khun (people) Lao etc etc