How long can i drive without a heater core and can the fume be harmful?

My heater core was damaged and has been removed from my car. Both hoses were sealed afterwards. I have a 1995 ford E150.

You can drive it that way as long as you like and the hose connections hold up but make sure that the two holes in the firewall which had the tubes from the heater core coming through them are sealed well or you might get exhaust gases if there's a leak or if the engine has oil leaks, oil burning smells or gases may get inside the van. Seal the holes with a metal foil tape used in home HVAC systems or dum dum sealer, rubber plugs, etc.

What fumes? If the hoses are sealed that's that. There's no safety issue only one of cold and condensation in the winter unless you have it replaced of course.

The sealed off hoses are part of the coolant system and may make the engine overheat. The coolant system is a sealed system. And those hoses are part of the sealed system

Until the temperature drops to below the comfort zone for you. If you have fumes in the passenger compartment they are harmful. Get that fixed As soon as possible.

As long as the hoses are sealed off so they don't leak you can drive it till the cows come home. You just have no heat, that's all.

No heat and no defroster but otherwise 100,000 miles minimum

You need to connect the two hoses together or your coolant won't circulate through the
engine. Then you could drive it for as long as you want to. But, like Paul says, plug
the holes in the firewall.