A1 and MO are the same thing. A1 is the AWS designation, while MO is a manufacturer's trade name. So while the can of electrodes may read E7018-MO for example, the AWS designation is still listed on the can (usually in small print) as E7018-A1. I wish that manufacturers would not do this as it adds confusion for some welders.
The H4R designation, which is explained well by the links from jwright650, is typically allowed to be exposed for a maximum of 9 hours out of the electrode oven before requiring a rebake, depending on which code is used and the company policy/procedures.
Chris