Answer
(Fatwa: 1041/1028/N=1433)
(1 & 2) Men cannot wear any kinds of socks in the state of Ihram in tawaf, sa’i and in any other time when they are in ihram. It is forbidden for males to wear socks in the state of Ihram. Yes, there is no harm in wearing the socks while doing tawaf when a man is not in ihram. In the same way if a man cuts the socks at the place of ankle and they look like slippers then there is no harm in wearing such types of socks in the state of Ihram.
قال فى الدر (مع الرد كتاب الحج 3: 495، 498-500 ط مكتبة زكريا ديوبند): وبعده أي : الإحرام بلا مهلة يتقي ……….لبس …….خفين إلا أن لا يجد نعلين فيقطعهما أسفل من الكعبين عند معقد الشراك فيجوز لبس السرموزة لا الجوربين اهـ
Allah (Subhana Wa Ta’ala) knows Best
Darul Ifta,
Darul Uloom Deoband