I would always use a tx. Had a situation recently when an arc denied they had any alarms from a site after a fuel theft. The adpro log proved there was alarms and images sent etc.
no you need to assign an address it may not keep its address if you disable dhcp. Also if you do disable it on the router then other devices wont work unless they are assigned a static ip manually
does your external bell ever sound, ie is the bell trigger connected or failed?
temp connect the bell trigger wire to hold off -ve and it should sound. If it doesn't you have an issue with your bell or cable. Then look at why the bell output isn't working.