• Time research reduces the time production runs take. I think level 20 is generally considered the sweet spot in terms of usability.

• Production efficiency reduces the amount of waste - and thus lets you produce the same amount of stuff for slightly less resources/components/etc. As with Time research, there are diminishing returns on higher levels. I think 20 is regarded as the sweet spot, but check the forums for specifics per blueprint.

• Invention is used to turn a tech 1 blueprint copy into a possible tech2 blueprint copy. This requires a lot of skills plus datacores. A succinct explanation of how the entire concept works can be found here.

• Reverse engineering is used with relics and artifacts found in archaeology sites, and can be used to develop specially modified hardware, as well as being crucial for tech3 ships.

• The reason publicly available slots tend to be full is because, well, they're publicly available -- and there are a LOT of pilots. Best bet is to join a player corp with their own stations and a research division.

• EDIT: This link on the forums has a lot of good articles to sort out what's what with inventions and industry in general, and this link in particular has pretty much everything you want to know about research in specific

The Dramiel is the fastest Frigate in EVE.

The Claw is the fastest of the Interceptor group, but a Dramiel running an MWD is faster because of its lower mass, since MWD speed boost is affected by ship mass.

Things that affect speed are

• Base speed of ship
• Low slots (using Overdrive Injector II¹)
• Mid slot (using one 1MN MicroWarpdrive II)
• Rigs (using Small Auxiliary Thrusters II¹)
• Navigation Skill
• Acceleration Skill (when using the MWD)
• Ship mass (when using MWD)
• Implant bonuses (e.g. the Snake Set)²
• Leadership and Gang Assist bonuses²

Here's a table with the calculated speeds (base ship speed, max fitted/rigged and MWD, each without skill bonus and finally with all skills at level V³):

Here are the results as CSV. They were calculated from a subset of the CCP database export with this Python script, using the speed formulas from the top speed calculation guide and the Aenigma formula for bonus stacking penalties. Some calculated speeds were cross-checked against Pyfa.

¹ The speed bonuses from the Overdrive modules and Rigs are subject to severe stacking penalties, making it fairly useless to cram more than 2-3 of these in your ship in total. However for the purpose of finding the fastest ship it was assumed that all ships had their low slots full of Overdrive modules and their Rig slots full of Auxiliary Thrusters. This is not a sensible build to fly around in though.

² These bonuses affect the velocity directly and therefore don't matter for a ship comparison. They were not taken into account here.

³ Due to neither implants nor Leadership/Gang bonuses being applied, this is not the fastest these ships can go.