I'd have to double-check, but I'm fairly sure Bloodshield puts a 1-turn shield buff, so, if you're worried about it replacing the A3 shield before you can use your A2, it's not really a huge concern. His typical rotation would be A3->A2->A1, and if you had bloodshield, when using your A2, I think it would use the existing shield and not the bloodshield-replaced one. Overall I think Bloodshield is probably a decent artifact for him to use, though not hugely so.

To your second question, yeah ultimately you should book his A1, because it does give fairly significant damage bonus, but if you're short on books it's not the end of the world to leave it unbooked for now.

I haven't paid attention lately, but Bloodshield is gear, so I'd think it would put up an artifact shield buff, which is distinct from a skill shield buff.  If that is the case, the shields from the Bloodshield will not intereact with teh shields from his skills at all. Icon on the left is a skill shield. Icon on the right is an artifact shield.

i