Conversations breaking up from iMessage on Macbook Air to iPhone

I have two specific issues:

Issue #1

When using a group chat from my iPhone, the conversation stays intact. When responding to the same group chat from my Macbook Air, the conversation splits into a different chat. I cannot figure out how to sync these conversations so that when I respond from my computer, it is within the same chat.

Issue #2

I updated my iOS to OS X (10.9.5) and now certain iMessage conversations with certain individuals do not transmit whatever from my computer. I get a red exclamation point. When combining an email address and a phone number and making a group chat with the same individual, the conversation transmits.

Please help me rectify these issues!

Thanks in advance.

Liz from Montreal