What are the chances of being approved a 3rd time with a waiver , for a K1 Visa?
There is no way to assign an exact "chance" to your case. However, when you submit your written request you should explain what happened in your first marriage and also explain that you withdraw your petition in 2014 and why. Submit any documentation that you think may help and supports your claims. Since the first one was a long time ago, over 15 yrs , there's a good chance of approval. However your second one was less than 2 years ago so you should give a good compelling explanation about what happened.
Does the US consulate investigate every marriage do they contact the registers office?
They may investigate the marriage. The consulate does not divulge information about whether they actually look into every marriage. However, if you are not legally married then it should not be an issue.
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