May a person who is statutorily eligible to seek an immigration benefit or waiver to prevent his/her removal from the U.S. be discretionarily denied the benefit or waiver based on conduct or convictions?

Yes. Even if a noncitizen applicant meets all the statutory eligibility criteria to obtain legal immigration status or to seek an immigration benefit and is not barred from doing so because of a determination of deportability or inadmissibility, s/he is not automatically entitled to the immigration status or benefit until s/he is found to be deserving of the status or benefit based on the discretionary review of such application by immigration-related authorities. Discretionary review may include factors such as personal character, family unity, length of time residing in the U.S., employment history, and prior arrests and convictions.