“I have been searching online for this issue if I can file my taxes as single because my spouse and child have not immigrated to the USA.”---> Filing your return as single is technically incorrect as you are married NOT single( though both single and MFS have the same marginal rates). You cannot file as single, you know, since you’re not.
“1) Based on my situation described above, can I file my taxes as "Single" or do I have to file as "Married Filing Separately"?”---> You can file your return either as MFJ or MFS as you were (obviously) married. You must be legally married under the laws of the US (that doesn’t mean that you have to be married here, just that we have to recognize it) so same-sex marriages are not realized for purposes of MFJ.
“2) If I can file as single, will the IRS say something since I already filed my past two returns as married filing separately with my spouses name and none EIN or TIN or whatever that is called?”--->Then I guess the IRS may treat you as single filer due to divorce. As you can see, you can file your return as single if you were never legally married under the laws of the US (meaning, really, that same-sex couples who might be married abroad must still file as single in the US); you were legally separated or divorced according to the laws of your state ,in states like Pennsylvania where there is no legal separation, this means your choices are only married or divorced, or you were widowed before the last tax year and did not remarry during the tax year.The IRS cares if you commit tax fraud or tax evasion. However, with the IRS, if they are LEGALLY separated, they are treated as divorced, as said previously, and single.They are married and can file MFJ or MFS.