Can I fly through a TFR?
Yes and No (of course it is an FAA question), If you are receiving flight following or on an IFR flight plan and was cleared through it. When I lived in FL the ones I had experience with were the Space Shuttle TFRs and those you canNOT fly through,. While in NJ there were often ones over the UN and those you can't fly through either.When I moved t California I was introduced to the fire/natural disaster type TFRs which you can fly through ..sometimes ...(I will not be doing so VFR).
91.137-91.39 states in great detail the hows and whys
The AIM has a chapter on Other Airspace that describes the differences in the airpaces and even gives examples of the NOTAMS that will be issued for them. At the bottom of this entry is just the begining of that reference.