Should I store things in corpses

Places you can safely store your items include any houses you buy, your companion(s), and your horse.

Places considered to be owned by you (and therefore contain safe containers) are (spoiler warning):

• Arch-Mage Quarters (after you become Arch-Mage)
• The Dawnstar Dark Brotherhood Sanctuary (After you've finished the Dark Brotherhood quest line)

I have personally stored items in my apprentice quarters in the College of Winterhold without problems, however others have had stuff go missing from there, so be careful.

Other containers may not be safe. Given what some other answers have said, Gerder's house does not seem like a safe place for long-term storage.

Bodies do not persist forever. Eventually they will be removed.

I was just beginning to think that the dragon skeleton at the College would be around forever, but when I visited it now it was gone.

Similarly, when I killed Belethor, I was surprised to see that his body had been cleaned up rather quickly.

Corpses tend to stay around longer than you would ever have need for them (I presume to give you adequate chance to loot), but they do disappear eventually, no matter their source.