1: Yeah, the secmage has to still scan the rooms 1 by 1. If he were to just fly through, it'd be like you driving a car and trying to see both sides alleyways in detail.
2: So he'll see the auras, but to study an aura in detail he'd have to roll assensing. I personally think that for the detailed assensing result, you need to assense 1-on-1. For more generic 'oh wait that's spells!', a single roll might suffice. Difference beween 'I'm scanning the crowd' and 'I'm looking at this guy in detail', basically.
3: So that's where we go into astral signatures, and Auras in general. So every Awakened person has a unique feel to them, and it is left behind as signature in their magical activities. I'd argue that a mundane person also carries a form of 'signature' to them, that can be identified. So if the guard rolls 3 hits, which is what you need to detect astral signatures, he then gets to roll a Memory test to see if he realises he's never seen it before. If the guy is constantly seeing the same people and properly scanning them, that'd probably be a threshold 2.
4: You actually do need to roll at least 1 hit to identify Awakened, so no, Awakened auras aren't brighter persé. However, you ARE correct that the spell has its own signature, so unless it's properly Extended Masked, it shows as its own aura. So yes, it's easy to spot 'hey that person has a spell or something on them'.
5: Having a Spirit warn you about an astral entity looking at you, definitely would help. If you want to disguise your aura and foci, you need Masking. To hide spells, you need Extended Masking as well. Those are metamagics you can get with Initiation.
6: Not just the animals. The trees too. The grass. The very Earth itself.
7: Yup, Materialized Spirits move slower than people, unless they use the Movement power on themselves. So likely a Force 4 Beast Spirit would use Movement and make themselves go at 20/40/+12 instead.
8: To track the guy, the Spirit needs to use the Search power. In case of a Beast Spirit, that's an optional one so you need to decide as summoner that the Spirit has that when summoning, can't change it afterwards. Then, every kilometre distance will raise the threshold with 1, so other side of the country is pretty much impossible for the Spirit to follow. However, if the Spirit initially got a bead on the guy, it could chase astrally. But even then it might fail to catch up: Coherent Astral Walk is 100m/CT, aka 120km/h. If the guy drives faster than that, the Spirit won't be able to keep up, at best it might switch to Astral Running, fly past, then wait ahead to try an ambush. And of course Materialization takes a Major Action, so the Spirit can't attack on the same turn that it materialized, and the guy can realise and try to escape.
9: Yeah, you can cancel an order (unless the Spirit hates you and doesn't want to), but no refunds/exchanges. Sorry, should have read the conditions on your receipt.
10: Kin/Kindred is the SR6 name of Man, yes. And yes, no Natural Weapon, no Energy Aura, so all it can do is cast spells, use powers, and punch people.