A refund is possible under EU-261 regulations and if the routing & pricing options you find now are appealing to you take it and run but make sure you will get 100% of it back, in writing, from Cheap Tickets or if DY billed you directed it should be easier.

You purchased through Cheap Tickets and they are your travel agent. This is what they get paid for (the commission on the ticket) so call back and calmly but firmly tell them to handle it. It is a good idea to propose option to them such as a different routing that is about the same price.

No they will not cover the hotel.

Upside is you have time for this to get done instead of the flight being this weekend.