[Is this a good Merc spec for PvE?]

For pure dps, move the 3 points from integrated cardio into hired muscle.

[Killing Admiral Shai (BH stroy quest on Ilum)]

I just completed this today after several tries. Once I had him down to about 20% and had 8 stacks of debuffs on me I just ran around until they wore off and then defeated him pretty easily after that.

[I find Merc BH a very tough class to solo with..]

I'm a level 44 arsenal merc, and I very rarely die, and usually that's only by my own fault. Mako does a pretty good job of keeping me breathing.