Heating Issues

Could be the core or the hoses. Hard to say without actually taking it apart to search out the problem.

If they are leaking at the core end it would make the floor wet, you would smell coolant and because it would leak into the heater box via the insulation it would fog up the windows. Same as a core leak.

This is a video on one method of it's replacement. (I would have moved the column or flexed the HVAC box to avoid the damage to the new core but this method does work) If you wanted to see if it was a core leak or hoses you could take out the panels and check, or even replace the core yourself.

https://www.youtube.com/watch?v=02AkPvT1bVg

Cost is hard to say, but going by the book time and the factory core price it would be close to $900.00 or so. (Now if you DIY and go with a less expensive core you could save a LOT of money) Check online for core prices, places like Advance Auto, Rock Auto, NAPA, O'Reily, and even Amazon.