I replaced the radiator and when the car gets hot it does not fill the overflow tank. I believe it is a bad radiator cap.

and now I see coolant leaking from the pump area. Could the water pump have been damaged from high pressure ? Does it need replaced or could it just be leaking from the weep holes ? It’s hard to see anything under the A I R module.

 

coolant leaking from weep hole in bottom of water pump means only one thing! you need a new pump!
as per filling overflow bottle. yes the coolant level should get higher with a hot engine. At no time should the bottle "Fill".
However, if your pump is leaking, you will never be able to burp all the air out of the system.
replace your pump if it's leaking! and so sorry to hear you have a A I R system.

 

Start with this directional video: It was not a difficult or expensive repair. But, take photos (cannot overstate) from several angles before you start - it helped greatly when I forgot how to position one of the adjustable brackets. Here's your chance to replace the (3) hoses (including the small bypass hose to the heater, and a chance to repaint the new water pump/bolts (GM engine blue) and the rear air pump/brackets (satin black). I prepped/repainted the fan blades a gloss black. Be most careful while disconnecting the delicate and irreplaceable air pump valving/solenoid assembly, and again, just take a picture of it before you disconnect it. Direct/insist the same to your Tech if you have it done for you. Finally, make sure your new water pump includes the gasket - some do not come with it or was not properly put in the box. The Tech in the video makes some good, time-saving points (i.e. be sure to RTV the water pump affixment bolts (only 4) that go into the engine block to prevent weep-age.
I thought it was a satisfying repair. Just spend quality time protecting the heck out of your fenders with cushioned fender mats, thick soft blankets or old bathroom towels. And, have a low pan/cardboard to catch the ~ 1.5+ gallons of green coolant that comes out in the process. After reassembling and refilling the radiator it still required significantly topping off the radiator (when cooled) after 3-4 ('burping') short drives.

Hope this helps.

D

 

One of the best ways to "burp" a cooling system that I have found after doing maintenance on it is this funnel arrangement. I love it and works great with no mess. Raise the nose of the car with jack stands, sloped drive etc... fill rad, attach the funnel and fill about half way up, heater on full, start motor and let it do its magic. Air bubbles will come up and it will self burp. Fill as necessary while running. When the air bubbles stop coming up, you are done. Put the plunger back in to remove funnel. Good luck and replace that pump.

 

I wish I knew about that funnel a couple of months ago. When I followed the shop manual's process to "burp" my cooling system it made a mess once the thermostat opened.