Yes, Personal Access Display Device
Yes, Personal Archive Detail Device
No, It's not short for anything.

Plasma is routed through the ship through EPS conduits. What is plasma?

Electricity
Synthetic Bioneural Energy
Electrically conductive ionized gas.

Cortical Stimulators are common in Sickbay. What does a Cortical Stimulator do?

Stimulates neural activity
Suppresses a person's conciousness
monitors a persons REM patterns

What is a Biofilter ?

A piece of technology that masks a person's biosigns
Prevents bios of senior officers to be retrieved when a
      ship is scanned
A part of the transporter technology that can be purged
      if dangerous substances are detected during transport

Hypospray is used instead of needles. How does the Hypospray work?

It's a well-kept secret
A small transporter device injects the medicine
Compressed air injects the medicine

What is LCARS short for?

Library Collective Access and Retrieval System
Library Computer Access and Retrieval System
Library Core Archive and Reserve System

Voyager needs a subspace field to be able to go to warp speed. What generates the warp field?

The deflector
The warp Core
The warp Coils

What part of USS Voyager contains bio-neural cells?

The gel packs
The Biobeds
The replicators

The Borg collective uses (insert name) to assimilate humanoids and to turn them into Borg drones.

Nanoprobes
The Hive Mind
Borg Exoskelleton

These things are located at the front of the nacelles and are used to collect particles that can be used as fuel. What are they called?

Bussard Collectors
Jeffries Tubes
Plasma Injectors