Yes, get it professionally done, soon.

Refill with a 50/50 mix of antifreeze and de-mineralized or distilled water.

The heater core should be OK, if you don't put this off.

Keep the radiator/coolant, expansion tank FULL at all times.

Air = rust.

thank you

If only best quality antifreeze is used, of the correct type (depending upon whether you have only a cast iron engine, a mixture of metals or an aluminium engine, but most are for all types nowadays, here at any rate. It alone will stop rust/corrosion starting/continuing. That is part of its job.

The reasons for rust forming in the first place are probably due to a poor quality antifreeze, wrong antifreeze, not enough antifreeze or none at all!

Too much antifreeze is also not a good idea, though the negative effects are less obvious. The lesser of the two evils......

Like lyn sez, get a pro job. Sometimes radiator cleaners can pool in heaters and damage them, it takes a pro to prevent that. If you are going to DIY, turn the heater off or even better bypass it for any cleaning. Rinsing with clear water is ok to go through the heater, just watch out with the cleaners.

The part I always have to watch out for when I flush is to have the radiator cap off when I refill. Don't fill it right up at the start, just put in enough antifreeze so you can see it. Then let the motor heat up, and the thermostat opens and the engine takes the water. Then gradually top the system off, watching the fluid flow by. Check again after the system cools off to see if it filled, then top off the resivoir to the low mark. When the motor is running and warmed up, see if the fluid in the resivoir is up to he high mark. If not, you can top off the resivoir.