Hi,
for the load balancing, please check your RIB to see if all prefixes have the same metric.
What about the physical links between A and C?
I don't understand the problem about AB and C load balancing; you could have that with OSPF (same metric) or EIGRP (with different metric too, using variance as you, or checking bandwidth/delay).
BTW the second link doesn't get down. Please check speed/duplex, and let me know.
In your eigrp configuration, don't use the neighbor command, and the best practice is to use the "no auto-summary" command, then select your eigrp networks; if you post more infos about your topology, I could help you).
HTH
Andrea