Edit: MHW does save to the cloud. Make sure you activated it and save your files on an USB stick to be sure. I did not once think about my MHW saves because every game I own saves to the cloud. ...

Does MHW autosave after quest?

Monster Hunter World doesn't have the autosave feature us gamers are typically used to. If you don't manually save before exiting an online multiplayer session or entering a different one, you'll lose all the gear and weapons you crafted, which can be somewhat annoying (an understatement).

Does Monster Hunter save after every quest?

The game will typically autosave once a quest has been completed or if players change the settings in the options menu. ... The game will also autosave if players upgrade their armor/equipment or forge a piece of equipment.