What should I do for my unconscious brother so that it may be counted in the balance of his good deeds, and is it permissible to perform Umrah on his behalf?

If your brother is completely unconscious, he is relieved of religious obligations. If he regains consciousness occasionally, he is required to perform his religious duties during his periods of awareness. You may dedicate the reward of good deeds to him, and it is best to start by settling any debts, Zakat, or expiations he may owe. Increase your prayers and supplications for him. Your Umrah on his behalf is acceptable if you have first performed Umrah for yourself.