Can't trade ships. Two exceptions: The special requisition boxes for captured enemy ships, but one of those is no longer obtainable and the other won't be obtainable until tomorrow. However, if you claim the ships, those also can't be traded.
The fastest type of ship is the Klingon birds of prey. Federation side, it'd be escorts, which are slower but more durable. Among escorts, the fastest are the Multivector Advanced Escort, which rivals BoP speeds when its separated, and the Tactical Escorts, which are the faster than the advanced escort in combined mode, but not as fast as the separate sections.