As far as the fan arguements, I'll leave it with 2 comments. I recommend pull, and a little bit here, a little bit there adds up after a while
Fans are usually designed for flow in a specific direction. They work better in that direction. Some also have starter or tach circuits or ... so it's best not to arbitrarily reverse them. It's more than just the motor.
Shrouds... plexiglass, tupperware, acrylic, metal moulding, duct work, styrofoam, aluminum sheet, old computer case (for the metal), blah, blah, blah. Go wandering through your garage, kitchen, local hardware store, Walmart with the idea of making a shroud and you'll be surprised what all you can find that is inexpensive and in some cases will even look good. If you have the space (looks like you do) then make it a several inch deep spacer.
Since it's a heater core, you might even be able to go to the local junk yard and pick up the "plastic" piece that mates perfectly to that heater core if you know what cars it goes in. Depending on what it went into, with a little thought and a hack saw you can have a custom molded shroud really cheap, especially if they have a damaged piece that has the end that goes on the heater core intact. Doesn't do them any good if it isn't usable in a car, lol.
Another possibility, have you ever looked at a central AC unit and how the ducting is mated to it? Another source of material. Tends to be inexpensive as well, easy to work with, and looks decent.
Really just depends on the "looks factor" and a little patience in finding something that meets what you want.
As far as your almost new parts, remember, you never know when they might come in handy