Network command by default will match only on exactly the same prefix and its mask in a global routing table and if it does not match anything from that table no routes will be placed into BGP table.
If a mask command is omitted from the network command the prefix in the table would have to be a classful network.
If auto-summary is used and mask was omitted from the network command, not only does the classful network has to be in the routing table but you also require at least one subnet of this classful route.
BGP advertises routes (one best route per prefix only , even if we use maximum-path command there is always going to be one best path) from its BGP Table rather than the routing table itself.
Also do not forget about the next-hop-self neighbor command that you can use in case no one is advertising that link between you and an ISP, else it will be unreachable I guess, unless there is like a default route pointing at the ISP (static routes are not great if there are multiple links in between and there probably would be, although I guess IP SLA could be used here). Just be careful if using EIGRP’s summary route as it has an AD of 5 and will replace an eBGP advertised default route
As far as I know you do not have to re-advertise already advertised route, this is probably the whole concept of BGP. As long as the reachability is maintained all you require is that the route is advertised by one BGP Speaker. Moreover an iBGP route can be freely advertised to any eBGP neighbor as “i” BGP learned route and the local AS will be prepended to an AS-SEQ of AS-PATH attribute and if I understand right it will also be added into AS-SET so it is much easier to prevent routing loop from occurring my friend and the next-hop address is another mandatory PA that has to be included.
Furthermore iBGP neighbors can not advertise iBGP learned route to their neighbours by default because this could lead to a routing loop, hence why we can use Route Reflectors / Confederations or Full Mesh (this last should not be used it is very troublesome I guess hehe).
p.s. This whole answer was a nice chance for me to do a little BGP reminder haha , thank you for this buddy