When a deposit is made at an ATM by local check how much do I have to make available the next business day? and when is the rest of the money come available. The same question on a non-local check?

You would need to pose this question directly to your bank. Your bank would have a schedule that covers this, and it could be altered by the time the deposit was made.

Availability of an ATM check deposit can vary based on Reg. CC and the cardholder bank's policy. Reg. CC gives outside limits on availability, but those vary depending on the type of check deposited as well as whether the ATM is proprietary or non-proprietary, on-premise or off-premise, and how often an off-premise machine is serviced.