Could the guild be cheating? It's possible but as hardcore GvG players have already said in this thread, what is going on doesn't seem to be that unusual to be assured they are. In any event you can use quicktime player to record your screen and you most likely already have that on your computer.
As stated by others, if I'm working in a team or with a partner and it looks like our siege will be broken I will either have them or I will myself preload the next siege army while my mate keeps fighting so I can resiege as soon as possible. If I am on the defending side I will preload a new DA and let my mate break the siege while I try to place another DA as quickly as possible before the resiege. Who wins? Whoever the lag is favoring that day.
I also don't see OP mentioning DAs and if they are manual or auto battling. I could have missed this info but if I'm taking on a 1DA of rogues or spears on my own I can do the 10 battles easy on auto with no replacing troops and probably, around 12 seconds. If I have a team with me? It would be as fast as the lag allows. I can't say they aren't cheating but I can say it seems like you're underestimating how fast a guild can go on auto.
I look at the log and his name is the only name on every fight. How is this possible? .
The only name on the log is the person who won the final battle. Not everyone who participated. As far as I know there is no way of getting a full list of participating players even on your own side. You will also only be able to see that name if it is someone you have a connection with IE friends or hood. In other cases it will just show the guild name, so long as they win or are on the map.
I know that's not the point of your post but the only part I know enough to answer.