Seven knew exactly how old the Rani was, and prior to LOTTL it did seem that Time Lords were properly synced up, ie there was no real question of them ageing at a different relative rate. Drax, for instance, puts the time since he's last seen the Doctor (or the time since they were at the academy, can't recall which) at about 450 years and seems to assume that the figure would be similar for both of them.
Possibly they use a local Wi-Fi or telepathic field to obtain information, or employ touch telepathy. It's feasible, though, that some kind of ocular technology could be used to send / receive information, hence River's comment about the Doctor's eyes. It does seem a little silly for her to say - based on Ten's appearance - that she's never seen him this young. Tennant has eleven years on Smith.
Apparent real-life reason: It had not yet been established that Tennant would be leaving soon.
Also, it's been speculated that Ten's regeneration was one of those time-can-be-rewritten things. Maybe without the Time Lords he'd have continued for several decades. This seems redundant given Eleven's apparent lack of ageing over nearly two hundred years, though.
ETA: If "Lord Of Time" doesn't intimidate someone, then a name based on the weather probably isn't going to. Stormageddon, of course, would be the exception. Maybe he's named after the Doctor.