Hello,
check from the messages options if you are sending the messages using your phone number as ID or your e-mail in case you are logged with your apple_id. If they receive your message splitted, probably you are using your e-mail as your id, instead of the phone number. There is no way to merge the messages for them.
As for the second issue i can tell you that there must be a bug somewhere. Some days ago i didn't receive iMessages from two friends. We figured it out hours later.
Now: if the iPhone can't send message via iMessage service, it automatically SHOULD send it again as a normal SMS after a while. This didn't happen to me, indeed after hours and hours (5 hour for one and 20 for my other friend) they notice that the iMessage delivery was not confirmed.
So why the iPhone didn't sent automatically the same message as a normal sms? I think that the iPhone don't sent the sms automatically unless it receive a confirmation from the iMessage server that the delivery is not possible. That's why my two friends had still the iMessage on a "waiting status" without confirmation and why sometimes the times that go from when you send an iMessage and when it get converted to an sms is variable. I had problems in the past sending iMessages: one time they where converted to an sms in one minute, other time they took 5 minutes, and under the Christmass holiday (i think because traffic) the iPhone sent it after 15 minutes. The day after indeed i had problem receiving iMessages too.
Thats why i think that it's a server side problem, about the iPhone handling the delivery status with the server. I wonder why the iPhone doesn't decide himself to revert a message to a normal sms and i think the answer is to avoid duplicated. If you sent an iMessage, and the server is stuck and your phone decide to send it via cell tower without telling it to the iMessage server, then when the server is free the recipient may have a double boring message...
For now you or your friend can just pay attention to the delivery status of the iMessages.
Sorry for the lenght, hope it can help.