Instead of buying an expensive flush, use a cheap oil of the correct grade for a few hundred kilometers, then change it. Or change it sooner than normal. Whatever.
Keep it simple, full synthetic 5W-30 is fine and is available, cheap, and literally everywhere.
All the 20W-40 oils you'll find are 4T motorcycle oils and they absolutely do not have the correct specification for your engine. Run far away from this fool mechanic and do not contact him again.
Check your wiring, hoses, and other rubber parts. Use fresh fuel, change your fuel filter.
You can't clean these aluminum radiators. If there are signs of rust, or that the system was ever run on plain water in the past, it's good practice to change everything with new OEM parts. Thermostat, water pump, heater core, radiator, radiator cap, all hoses. Your engine is the other half of the cooling system, and if used on plain water, the entire system needs to be flushed. Easy to do at home, look up the 5 million times it has been mentioned on this forum with detailed instructions.
Do not fill the system with any kind of water under any circumstances other than an absolute emergency, or if you just temporarily need to get the car from A to B while you're waiting on replacing all the cooling system components.
Buy the right coolant for your car and use it correctly.
You can either replace all the cooling system components in one go, or by the side of the road as they fail one by one.
Change your rear main seal while you're here, even if it's not leaking. Be sure to get a quality new OEM or aftermarket part. No used seals!
This is a scam in most cases unless there's significant buildup of gummy residue, varnish, or rust inside the tank.
Change your in-tank fuel filter while you're here.
Change your cam and crank seals, as well as your water pump, while the timing belt is off. Use new parts only. Don't reuse the old tensioner. Also a good idea to get a new genuine timing belt. Beware, the market is full of fakes.
The timing system is another place you should not cheap out in the slightest.
Before tossing a perfectly good alternator, check the wiring that goes to it first to verify that the alternator is indeed the problem. The market is full of scrap alternators, nobody has a way to test them other than installing them, finding out they don't work and wasting your time. Finding a new OEM alternator is not easy.
Check and replace your battery terminals also if they're old and corroded.