Does the same reward promised in the Hadith "Seven whom Allah will shade with His Shade..." apply to someone who rejected committing an abomination with another man out of fear of Allah, and is someone who dies while shunning acts of perversion considered a martyr?

Your question about whether someone who dies having abstained from homosexual acts is considered a martyr, perhaps you are referring to the hadith: "He who loved, then abstained, then concealed it, then died, is a martyr." This hadith has been judged by scholars as fabricated (a lie) and not authentic. The designation of martyrs requires a legal text (from the Quran or Sunnah), and there is no text specific to someone who restrains themselves from lusts.

However, whoever restrains themselves from lusts and patiently endures it is promised a great reward; as Allah says: (Indeed, the patient will be given their reward without account).

As for the hadith, "And a man whom a woman of high status and beauty invited to herself, but he said: 'Indeed, I fear Allah,'" the Permanent Committee was asked: If a woman of beauty alone invites a man to forbidden acts and he refuses, will Allah shade him under His shade? They replied: "If a woman of beauty invites him to indecency and he refuses out of fear of Allah, then he has done good, and he will have a reward from Allah by His grace and benevolence, even if she was not of high status."