Rebuttal: The way that DeepOnion "drops" coins is a classic signature campaign. It has nothing to do with an actual Airdrop.
Claim 2: TOR integration gives "complete anonymity" and is valuable feature.
Rebuttal: TOR is not even close to completely anonymous2 and this was done/attempted by several coins long ago.
Claim 3: 100% anonymous.1
Rebuttal: TOR itself is not completely anonymous which destroys this claim anyways, and there is no known "100% anonymous" coin.
[1] - Both claims are made in their (misleading) signature advertisement.
[2] - Some past attacks: Weak Debian keys (2008), OpenSSL Heartbleed. Attack on Relay nodes (2014). Also read the following: Users Get Routed:Traffic Correlation on Tor by Realistic Adversaries
There is more, but this isn't a paid lesson in security. I'm sure that even the developer has no idea about most of it (and I do not mean the trivial and widely known stuff like Heartbleed). Remember that developer != cryptographer != security expert.
Do indulge me by telling me that TOR is 100% anonymous.
In theory, the best way to use Tor for an anon-touting crypto is entirely within Tor as a hidden service. The main problem that I can see, is that the blockchain is a matter of public record, and any transaction is roughly timestamped by it. An entity that wants to de-anonymise transactions presumably has a list of ips using Tor at any given time, and can compare that to the blockchain. At the very least the ips of some of those using the crypto could be narrowed down (if not outright determined, possibly even matched to specific transactions), given enough time.
The best way I can see to deal with this? Become a middle relay yourself, such that you are always on the Tor network, sending and receiving other peoples data, thereby cloaking your activity. There is potential to obfuscate when you do a transaction via time-delayed transactions (the point being that your ip is not on the network when the transaction goes through), but I can't see how to do that without the blockchain knowing of the delay (making the delay pointless for obfuscation purposes), without trusting a third party to relay a signed message at some future time (which is obviously not a solution).
As to how DeepOnion uses Tor, I don't know. Almost certainly it doesn't make wallets act as middle relays (so if you plan to use DeepOnion anonymously, I recommend you take the initiative and become a middle relay yourself), hopefully it does work 100% within tor (with things like dedicated onion servers for initial and fallback peer discovery, as I say I don't know).