Pyramid: Go down the side
Do not jump through the central blue terracotta. Make stairs down the side to the four-chest room, light it and locate the pressure plate in the center. Remove the plate, then carefully open the floor and collect the TNT. Reference: Minecraft: desert pyramid.
Before turning off, do not throw things on the furnace and do not lead a mob there. Clean the suspicious sand of the archaeological room with a brush, maintaining support; mass shoveling will lose finds.
Jungle Temple: Look for the trap chain
Inspect the corridor floor before stepping forward: tripwire between hooks triggers an arrow dispenser. Shears let you remove tripwire more safely; you can also approach the dispenser from the side and take its ammunition. Do not break a hook while standing in the line of fire.
Check the second trap line behind the first chest. A decorative riddle with levers does not automatically disable everything dangerous in the temple. Mark the already neutralized corridor with a torch and a sign.
The next related step is discussed in detail here: Exploring an ancient city: wool, chests and the Warden.
Other structures need different equipment
In the mine, do not run through the web to the cave spider spawner: poison and several enemies may block the exit. Light and approach from the side, maintaining cover. Silk Touch does not carry mob generator.
For the monument you need air and a plan against Mining Fatigue, for the ancient city - wool and vibration control, for trial chambers - separate keys. Record entry coordinates with Y: the closest point on the surface does not indicate a safe vertical descent.
Suspicious blocks are cleared according to separate instructions: Minecraft archaeology: brushes, suspicious blocks and safe digging.

