1) In the research screen, from either late DL or DA onward, it shows you how much you are currently spending on research that turn. This apparently does not take into account any racial bonuses (including mining a research resource), nor does it take into account that half of the bonus is free.
Alternatively, you might try looking under Timeline in Civilization Manager and you should be able to see your previous turn's research output-although in testing it seems to be two turns ago, as it takes one turn to process it and it can't be the current turn.
A better idea might simply be to look under Research in Domestic Stats and see 1) how much you're spending on research and 2) how much you're spending on bonus production/research. The two problems with using this approach are that, firstly, half of the bonus production is free while you pay for the other half, and secondly, if you are on anything other than 100% research funding (even if you have planets focused on social/military while research funded), you will see bonus production numbers added to this, because the Domestic Stats screen does not differentiate between bonus production and bonus research-which is unfortunate.
2) 18 is a bad example, but we'll use it anyway. Assuming your entire empire consists of one colony (not your homeworld) with, in TA, an initial colony for 14 research and a lab that gives you 4 research, you could have an empire-wide capacity of 18. At 100% funding for 18 research (flasks), it will take you 10 weeks for a 180tp tech. If you have your homeworld (24 research) with 12 research worth of labs on it, you can achieve 18 flasks/week or 10 turns for the tech in question at 50% funding (assuming 100% of it is to research-above example is 100% research as well).
Is that clear enough?
3) Because you have researched Planetary Improvements, which gives you a 10% social, 10% military, and more relevantly, a 10% research bonus. Since your total output is 26, we multiply 26 by 1.1 (100% + bonus) and arrive at 28.6-but final numbers in GCII are truncated, so we're left with 28.
