I don't think native English speakers would use "I will look forward to." I don't think it's technically wrong, but it is very old-fashioned. We would just say "I look forward to" or "I am looking forward to".

I think in general "I will look forward to" is wrong. It is "I look forward to". I will look forward to means, "In the future, I will anticipate something happening 'Even further' in the future." It sounds very strange and unnatural.

no difference, they mean the same, but 'I will look forward to . .' sounds more formal