Lump sum of child support and sole legal custody
2 attorney answers
Child support is intended to meet the ongoing daily expenses of the child. Even if the Father agreed to pre-pay child support in a lump sum, it would be disfavored by the court because there is too much risk that the money may not be used on daily needs of the child and/or run out before the end of the time period it is intended to cover.
You won't get a lump sum of child support for future support unless father agrees to that.
Him being in China and using email/phone calls/skype is perfectly normal, and in all likelihood would not let you get sole custody. To terminate father's contact, you have to convince the court that it is damaging to the child to let contact continue, and I don't get that from your facts.