Due to good game design you can get the items mentioned in the title immediately after completing museum through really simple cheese.
First off, you’ll need to unlock the redacted chamber by throwing it into the reclamation bin in the museum level. Then you need to go into it and complete the battery puzzle. Once that’s done, go through the big door you just opened and enter the void doorway. Once you are in the fan room, drop through the fans and you’ll land back in the main room where you started.
Repeat this until a you see the boneworks box spawn infront of the fan room. Break it and take the handgun range module (if you don’t have it yet). Now when you drop down into the room, there should be a reclamation bin high up on the wall. There should also be a newly spawned boneworks box containing the dev manipulator.
Now using the radial menu, spawn in a utility gun (should be there by default since it’s a sandbox level) and pick the breakable boxes. (you want breakable since if you mess up you can just destroy them to clear the space and try again)
Getting to the Bin
This part is relatively simple. First pick up the dev manipulator and holster it. Next, stand in front of the bin such that if it was at eye level you would be infront of it. Then all you need to do is jump then place a box beneath you at the apex of your jump. If done right you should now be on top of the newly spawned box. Rinse and repeat over and over until you are infront of the bin. Then simply put the utility gun and dev manipulator into the bin.
Completing the Level
Once you’re done with the previous step, Go through the void door a final time and you will be teleported to the hand gun time trial stage. Simply complete the stage and it will put you back into the main menu. With that you should now have the utility gun unlocked and be able to spawn it through the radial menu anywhere. Once you have the utility gun you can also get all of the items normally locked behind expensive ammo purchases in the tower by just spawning yourself the necessary ammo.