Well for starters, he isn't smart by splitting iden from inferno seeing as one of the sole advantages of running inferno vs. imp spec forces is the retinue keyword. 
Aside from that, don't chip Bossk. 1 or 2 hits on him while he's sitting pretty in heavy cover are exactly what he wants you to do. Focus fire on him only when he's in the open and you're sure you can kill him in 1-2 turns. He rolls white die so his defence is miserable when focused, especially vs. clone fire support. 
 Save your "Call me Captain" card for this move. When you anticipate he'll rush you (and it seems you have when that is down pretty well), play this card and Rex will turn into one big range 1-2 "**** you" ball (you add three red dice to every attack within range of Rex) and you can make him sorely pay for any close advances. You might consider even waiting until you're engaged in melee to play that card, seeing as Rex can add fire support to melee attacks with this card.
One last command card tip is to use "Take that Clankers!" to either focus down Bossk or the AT-ST since you'll match their range.  This could be especially useful on Bossk to punish him when he thinks he's safe to have a free range 4 shot. 
 
Overall this guy sounds like overconfident trash if he's willing to brag about victories and fail to check the rulebook. You got this

If you're going GAR, stupid as it sounds a second (or even third) core set would do you well for more Phase Is as its the cheapest method of getting them (plus getting you a load of useful dice and tools not to mention triple BARC). Aside from that, Captain Rex is still a **** hero on all tables. Phase IIs will net you some additional corps options, and ARCs (though hard to find sometimes) are invaluable in every way from strikes to full squads. 
CIS is pretty much the same on wanting more core sets as B1s are your friend. Past that it's kinda the wild west because most CIS expansions are pretty dope.
Not specific to GAR or CIS, you'll want the Upgrade Card pack for additional options. Tbh though, you should feel free just to write these down next to your unit cards in casual games. In league games though they might require the real card. 

The reply above has a good point on objectives. If anyone is playing AT-ST they won't have as good an objective bid as you will most of the time. The AT-ST will try to thin your units as much as possible so his corps can get in late game and seize objectives. The three major strategies I'd suggest you take are either trying to focus down the AT-ST as soon as possible with impact spam (having the dork actually build the model will help with LOS), seizing the objective (the middle objective if it's intercept) early and then clone castling up and fire supporting the crap out of the AT-ST and whoever gets near, or lastly forcing the AT-ST to choose between two attacking groups while the one it doesn't focus on flanks his corps. 
Don't waste your time on bossk unless he's out in the open, if you catch him making a risky play with bossk, punish him as much as you can that turn because the crit lizard is more fragile than he seems. That also said, save your AP rounds for the AT-ST. 

Not at all. Look for the blue text and review that. List building websites will take care of the hard part (point changes and errata) for you. 

Not at all. Look for the blue text and review that. List building websites will take care of the hard part (point changes and errata) for you. 

To be able to resolve the abbility of the card you have to expend it. It doesn't matter if you use it for 1 mini or all, you're using the upgrade so you must expend it.

Could you tell us some of your ideas about strategy with this list? That would help clear up which choices are sound. 
Imo, you should drop the HH-12, Medical droid, and maybe even the naked scouts for DLT-19s on some or all of your stormies. Getting a command card like strict orders and/or commanding presence should be a priority too. Even with the E-Web I think your gunline is too weak to stand on its own with so few range 4 weapons. Besides, 11 activations is perfectly workable.