You may be eligible for employment authorization while your asylum application is pending. The application must be pending for at least 150 days excluding any days you caused a delay. There also must be no final decisionon the matter.
I would hope you have researched the oddities and negatives to asylum prior to filing. If asylum is granted, you will not have to return to your native country, you are eligible to work in the United States, you would be eligible for a travel document, and have a other to lawful permanent residence and citizenship. The negatives are if granted you would not be able to return to your native country (without risking the loss of status) and can be ordered removed.
You should not enter into a marriahe unless you jntend to bud a life together. You can pursue both a marriage-based adjustment of status and asylum. Adujustment id status would redult in lawful permanent residence. The marriage would likely be scrutinized depending upon the stage when you pursue adjustment of status. You may also need to seek reopening.
It would be in your best interests to consult an experienced immigration attorney as soon as possible.
Your question appears to be about employment authorization but then you end by asking more broadly about marriage adjustment and your other options. It is very important to address these issues in a consultation w/ competent immigration counsel. Many Avvo attorneys offer free consultations so check the site and their profiles carefully. Answering these questions in a general way in this venue is not possible. We would need a lot more factual background. Be sure to never file a frivolous asylum claim. Whether a claim is "frivolous" or not can be evaluated by an immigration attorney. Whether or not adjustment is possible or what your other options are is another question that will depend on a variety of factors.
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Two types of situations. Asylum filed timely and no delays caused by you -150 days after your original filing you can seek EAD. Defensive asylum - no EAD eligibility.
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