How can a divorced woman whose father has died and who has no children or full brothers marry someone of a different nationality who is suitable for her, despite her half-brothers’ rejection of him due to his nationality, and without resorting to courts to avoid problems? And who would be her guardian in this situation?

If the suitor is religiously and morally compatible, your guardians have no right to prevent your marriage. The difference in nationality is not a legal impediment. Try to convince them. If they insist on refusing, the guardianship transfers to the next in line among the guardians, such as paternal uncles or their sons. If all guardians refuse, then take the matter to a judge so he can marry you off or compel your guardian to marry you off.