0) Traded techs DO trigger tech inflation. Whether they trigger it on the turn they're obtained, I don't remember, but at the very least by the next turn.
1) Tech inflation occurs in DA as well (I think even DL but it's been so long I can't remember), but functions differently: You get a certain amount of "free" techs (that is, not inflated)-somewhere between 30 and 50 if memory serves. After that, individual techs increase it by 1 or 2%, in general, whereas completing a tree or sub-tree adds another 4 to 6%. However, DA inflation caps at ~270% (starting from a base of 100%), again assuming I'm remembering correctly.
2) In TA, your first ~15-20 techs are inflation-free, then there is a roughly 40% increase for non-military techs, and about a 100% increase for military techs (military techs being weapons and invasions, but, suspiciously, not defenses). Then after another 10 or so techs (25-30 total), it jumps from the previous 1.4x/2.0x to 2.1x/4.5x. The last jump is between 50 and 60 total techs, taking us to roughly 2.8x/6x, where inflation stops.
The above is taken largely from Jacklv's own work on tech inflation, with several tests to confirm ranges rather than absolutes, as absolutes are much more difficult to nail down. But any errors are my own.
3) Techs with the same XML cost in TA cost more than in DA, even if they're the same galaxy size and tech rate, although I don't have the numbers on hand. What this means is that (for example), if the XML files and Galactopedia report that a tech costs, say, 1000, in DA/Gigantic it will take ~600 research to get on very fast, whereas it'll cost somewhere north of 900 research to get in TA/Gigantic or somewhere north of 1000 in TA/Immense, also on very fast.
Also note that all of the above doesn't even take into consideration the extra 50% ingame tech cost of "military" techs (weapons and invasions, but not defenses) in TA.