Coolant leak?

Recently my car was running a little strange, shortly after I pulled it over to check it out, coolant mixture started pouring/ spraying out underneath. I had it towed to a mechanic, they said my radiator had exploded and had it replaced. I asked them if they had checked out anything else like the water pumps or thermostat, I don’t think they really looked at anything else, but seemed confident the problem was due to damage to the radiator in an accident a couple years ago.
Was running fine. Shortly after, after a weekend that included a trip almost 300 miles each way followed by several short trips around Philadelphia city streets, I noticed a noise after I parked my car that seemed like a boiling noise coming from under the hood. I was about to leave on a 1-2 month work assignment early the next morning so decided to leave it alone. On a visit back trying to get the car started (bad battery, I’ll need to get it jumped when I get home again Friday) I noticed the coolant tank is empty.
Normally I would assume all this was due to loosing coolant, but the temperature dial has read normal through all this. So my questions are:
Is it possible to loose coolant to the point of major radiator damage without it telling you its overheating?
Is there a way to check the source of the problem myself before going to a mechanic?
How much money can I expect to invest to diagnose and fix the problem?
How hot does the engine run, is it safe to fill it with just water for short drives until I get it fixed (highs around 85 this weekend)?
I drive a 2003 Neon with about 110k miles