The base cost for research

• 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

Only indirectly.

The basic invention process does not take on any researched attributes of the BPOs or BPCs.

The only attribute of the BPC that affects the BPC output in the invention process is the number of runs on the copy. Generally you will either always want to use 1-run copies (mostly when inventing ships) or max-run copies (mostly when inventing modules or ammo). This comes into play when you use decryptors (or choose not to use one). These affect the invented Material Level, Productivity Level (Manufacture Time), Runs of the invented BPC, and invention chance.

However, there is still an indirect effect of ML/PL on BPOs. Usually when you make a T2 item, you have a few input products that need to be made which are consumed to make the T2, such as a T1 version of the item, and Construction Components such as Tungsten Carbide Armor Plates or EM Pulse Generator. Material levels on these BPOs mean you'll usually need to use less Moon Materials or other materials, which could lower your final cost of making the T2 item.

Putting all of these options together to figure out which is the best option to maximise profit is the interesting part of T2 manufacturing.