Yes, it will record from standby, but unlike other DVRs it actually comes fully out of standby to do so. In theory, it then goes back to standby afterwards, except when it doesn't.
You can record two channels while watching a recording. You can even watch a third channel at the same time, if it's on the same "mux" as one of the other two channels, and watch a fourth channel with Picture-in-Picture!
You need recent (latest?) firmware to receive OADs. No guarantees, but several people who bought Toppys recently have reported that they came with the latest firmware already installed.
Jumping to live only happens if you are watching the thing that is currently being recorded. If you're watching something else, you don't get interupted, at least that's been my experience.
You have to "pad" (add time to beginning/end) recordings manually, unless you load one of the TAPs that does it automatically.
You can have multiple, named favourites lists (e.g. for different users of the DVR), or you can completely delete channels so that a rescan is required to get them back. Channels retain their LCNs. One drawback of favourites lists is that TAPs can't make use of them. So I've just deleted all the channels that I don't want.