Honestly, we suggest postal for the FLR(M)'s and in person for ILR, but it is a personal choice.
Our most recent postal app was approved right at 4 months, so that's good. But they CAN take up to 6 months.
Yes, you can send a photocopy of your husband's passport. It needs to be a copy of every single page, which is a bit overkill, but that's what they require.
For your child, they have changed this slightly. You now need to include a letter addressed to your child at your address within the last 90 days before your application date to prove they live with you. If your child has not received any mail, you can include a letter from your GP confirming the child's registered address. They will likely charge a fee for this.