Travel In Different Directions

Several kinds of travel as yet exist only in science fiction:

aircars;
faster than light (FTL) interstellar travel;
instantaneous transportation;
teleportation (which might be at light speed);
time travel;
travel in other directions - between timelines, universes etc.

As usual, I wound up with a longer list than expected when I started to write it.

In Poul Anderson's Time Patrol series, in 19352 AD:

"'...the various governments were pawns in a galactic game. The time effect was the by-product of a search for a means of instantaneous transportation, which some of you will realize requires infinitely discontinuous functions for its mathematical description - as does travel into the past.'" (Time Patrol, p. 9)

Especially in an Andersonian hard sf context, the phrase "...galactic game..." strongly implies FTL, although this is not made explicit. Thus, people with FTL (we think), seek instantaneous travel and find time travel, in fact space-time travel which therefore includes instantaneous travel - if the traveler changes his spatial but not his temporal coordinates.

We have already asked why Everard and Whitcomb were trained to handle spaceships if, at that stage, they were expected to work only in their own 1850-2000 milieu. But other questions arise about space travel:

Surely there will be many different kinds of spaceships in future eras?
Both for training and for operations, the Patrol has large spacecraft in past eras so they must be able to move such large objects through time?

For story purposes, we see only timecycles and other small vehicles moving along Earth's world line. In the future, they must have spacecraft that can transport prisoners instantaneously to the (extrasolar?) exile planet and that can also travel to the Oligocene to be used for the training of Time Patrol cadets. The possibilities seem endless.