Either 256 or 65536?

I think I may run out of the 256 NAT IP's due to virtual things. If I change the netmask to 255.255.0.0, does all 192.168.0.0 ~ 192.168.255.0 becomes one network? Can I make, something like, only 192.168.0.0 ~ 192.168.10.0 one network so that I can have maximum 2560 hosts?

you can use this ip subnet calculator to help you.

using the mask 255.255.240.0 you'll cover from 192.168.0.1 to 192.168.15.254
Number of Usable Hosts: 4,094

Isn't this enough for you ?
Subnet Mask: 255.255.248.0
Usable Host IP Range: 192.168.0.1 - 192.168.7.254
Number of Usable Hosts: 2,046

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The OpenWrt netmask can also be configured with CIDR notation like 192.168.0.1/20 instead of a 4 number netmask. Leave the netmask field blank when using CIDR.