TOH: Rifthopper Shift Space and Speed

[prime sigil]

Sorcerer Rifthopper gets the feature, "Shift Space" which states, "you can spend an amount of movement equal to up to half your speed and teleport to an unoccupied space you can see within a number of feet equal to the movement you spent."

How do bonuses or additions to your speed or movement on your turn affect this distance? Do Boots of Speed from the DMG allow you to teleport twice as far with Shift Space as these boots double your walking speed? Does Unarmored Movement, such as on Monk, which gives +10 ft of speed increase the distance you can teleport? What about spells like Haste or Zephyr Strike that temporarily increase your walking speed? Could you use dash on your turn to double the distance potential covered by Shift Space?

Thank you very much for any additional insight.

Book: Tome of Heroes Page 130

[raw cave]

Your speed is a stat, like your AC or your Prof bonus. It is whatever it currently is; if something temporarily or permanently changes it, that’s what it is now.
This just lets you use half of it as a teleport instead of normal movement; it doesn’t increase the distance you can cover. Note that grappled and restrained both reduce your speed to zero, making this much less useful than, for instance, misty step in those situations. Of all the specific questions you asked, Dash doesn’t affect your speed, the rest do.