Board Thread:The Reference Desk/@comment-1783865-20170314090644/@comment-5.2.105.85-20170314094704

Unless there is a perception filter (like the Tremas Master used on the Fifth Doctor) Time Lords often know each other (as was explained in The Sound of Drums).

The First Doctor may not have noticed straight away, whereas the Second Doctor did.

I don't really understand your second question, however the Fifth Doctor could operate the Tenth Doctor's TARDIS in Time Crash.