All of those lights should work fine with those cells, I personally lean towards recommending LiFeP04 RCR123 cells in these applications because there are less components to fail (no voltage regulator, no protection circuit). The LiFeP04 chemistry is totally safe and robust. No need for the extra circuits, just top off frequently, try not to over discharge em.
I couldn't find any information on the NiteCore extreme as the website I found for em does not seem to be entirely working right, and the 2 distributors I found have websites under construction so again, no way to see the specifications.
The TK10 will have much better runtime if you buy a set of dedicated 3.7V protected RCR123s and charger for it instead, and I'm kind of guessing that the NiteCore extreme might also be compatible with a 3.7V cell, but have no way to verify that unless I can find a link somewhere to some detailed information about it.
The 3.0V cells you have linked to are actually 3.7V cells with a voltage reducing circuit built in to make them more compatible with CR123 devices. One of the main problems with this is that the charger charges to 4.4V instead of 4.2V like other 3.7V cells in order to overcome the circuit in reverse during charging, seems to me that if something went wrong with the circuit (like it shorted out or something), then the charger would be free to overcharge the cells pretty substantially. Another problem is if you ever add more li-ion cells to your collection in the future, then you need to really make sure that the charger for the 3.0V regulated cells gets used for those cells and those cells only!
The LiFeP04 charger terminated at 3.6-3.8V, so having it around and accidentally using any of the other types of RCR123 in it would not be hazardous, it just wouldn't complete the charger. Accidentally putting a LiFeP04 cell into a charger designed for 3.7V cells (with termination at 4.2V) is also reasonably safe as LiFeP04 cells tolerate overcharge reasonably well.
Eric