Hello, my name is ***** ***** I will be the immigration attorney helping you today.
Yes, you can apply to extend your visa using form I-539. Even if your extension request is denied, if you remain here and marry your boyfriend down the line, he can petition for you for your green card once you two are married. This is true even if you end up out of status.
Yes, it is possible for him to file for your green card immediately even after your 6 month extension as long as it was not your intention to remain here and have him petition for you when you submit the application for extension. If you decide suddenly AFTER you submit the extension request for him to petition you, then legally it is fine for him to petition you.
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