If the target of Engage declares an Attack of any kind, including a CC Attack, against the user, and wins the Face to Face Roll, then the user receives all pertinent impacts and makes his ARM/BTS Rolls without moving.
As @Triumph pointed out, you must take your ARO as soon as you are able or you lose it. Delaying against camo markers has it's own restrictions, so you might want to reread those bits. That said, Sixth Sense does allow you to hold your ARO against troopers in you ZoC so you can make the best ARO choice when the time comes.
If opponent declares Engage, he's only hurting himself really. If he loses, he eats a hit. If he wins, he is being placed where you want him. The only scenario where he wins is if you declare Move-Move and he fails his Engage ARO. Or if you were using something very valuable against him. But since it's your active turn, it's you who decide most of the time.
Yes your opponent choose where you are but once in CC you are quite harder to shoot (-6 agains standard weapon, no template weapon) Example : I had Achilles once being flammed by Scylla's bot. Engaging allowed him to avoid being burned and protected him from futher burn because he was in CC and untargetable by template.
Yes, you are right, but IMO doing that with expensive model against attacking chaff (I would consider scyllabot to be one in this situation, especially compared to Achilles) means the opponent will be very tempted to do what was described above (tossing you onto the wall), locking out your S2 TAG in limbo until scyllabot is violently removed. RAW they can do that, so... If you decide to agree not to do that (and/or if/when errata arrives), then of course a strong piece can afford being tossed around a bit as long as that template is the most menacing thing in its vicinity.
I feel like alot of the warband models like Shaolin and Morlocks are good candidates for Engage, because they almost always cost more than what they're jumping into and they stand a pretty good chance of messing them up in CC.
It's particularly true if you need to stop the thing you're Engaging. A Chain Rifle won't stop a HI, there's a fair chance they can just ignore it and keep going; whereas a successful Engage can stop the rambo (or at least delays it while they get rid of the engaging trooper). The other amusing one is HD Engages vs the second Short Skill or when your victim already has another FTF to worry about. There's a story of someone counterdeploying a Ninja MSR on an obvious TO Sniper position. Their opponent revealed a Dasyu (or similar), and they Engaged with the Ninja.
Yeah, I can agree that concerns about Engage are mostly relevant for situations when expencive CC monsters engage mooks. On the other hand, throwing chaff at powerful pieces is probably still worth it. Worst case, your low cost dude will still either waste half an order for the enemy. Sometimes it's the least, but solid thing you can expect them to do. Hm. I may be wrong here, but with this particular example there doesn't seem to be a room for engaging on the second skill declaration. If HD trooper activates right where your ninja stands, you'll likely need to declare ARO immediately (so, after 1st short skill) or lose it. Am I missing something?
I can see it for the sniper, as the player might declare BS Attack first (or be reduced to choosing between a pistol agains the Ninja and a distant target), but an Engage from Hidden Deployment against a second Skill of an Order is almost impossible.
First move is outside of LOF and the trooper has Stealth or otherwise doesn't trigger a ZOC ARO. Second move is inside of LOF and 2"+Kinematica. Edit: for clarity, I'm talking Engaging out of HD. Not Engaging HD.
That was my point. The problem is that engaging after 1st skill means the opponent can always correct his position to do something unpleasant to your potentially 40+ pts piece. When you get an ARO after opponent's second skill declaration, you can clearly see where exactly he can or cannot shove your trooper should you succeed with your roll. Although having your opponent in position where he isn't in range of any walls or other engagement hazards is arguably even more rare than catching him on his second skill declaration.