Terraria – I can’t seem to transfer a Terraria character and world to a flash drive

Since the only way to run Terraria on Ubuntu is through WINE as Ben Brocka and lunboks have suggested, I will answer your actual question, assuming that you are using WINE and if you are not, I would suggest that you revise your question to provide more information about your setup.

While I'm sure you knew this if you backed up your files, but to provide background for the answer, as per this question, the default behaviour is for saves to be in My Documents\My Games\Terraria\Players and worlds to be in My Documents\My Games\Terraria\Worlds as stated here.

You will want to put your character and world files in the paths mapped for My Documents\My Games\Terraria\Players and My Documents\My Games\Terraria\Worlds respectively. The default WINE behaviour if I read correctly is for My Documents to map to your home directory so it would be home/(user)/My Games/Terraria/Players and home/(user)/My Games/Terraria/Worlds for your respective username I believe. If you want and this is up to you, you can remap where My Documents maps to in wineconfig, but you will have to adjust where you put the save files accordingly.

You don't drop anything when in a PvP, but there may be a tShock plugin/feature that allows this. I recommend you check out tShock here.