I did remove the battery when I connect it back the car does start but not iddling

Make sure that all the vacuum lines are hooked up correctally and that there are no other vacuum leaks

Take it back then, should be still covered if diagnosed with same issue

it looks like your IAC (iddle air control) is failing you could try removing and cleaning it with carb cleaner to get the dirt out that is clogging it. or you could buy a new one. That valve make that the car iddling even without oscillations.

usually when a car wont iddle it may have a blown head gasket , remove oil filler cap on rocket or tappet cover check for creamy coloured oil , if so blown head gasket , also when morot is cool remove radiator cap and check fro brownish residue under cap if so blown head gasket .
remove each spark plug if one or more of them is white on tip of plug water is getting into cylinder ..

if none of these some carby's or throttle body's have iddle screww which can be adjusted to speed up iddle , or if throttle body it may have an iddle soleniod which may need to be replaced ,
i hope for you is is just and iddle issue , both the solenion and head gasket arnt cheap to fix.
the soliniod although easier to remove and replace its cost is usually .... expensive on most makes of cars , dont know why just because there greedy dealerships !

hope you need only to adjust carby or check timing is o.k

good luck hope this helps

take some baking soda or coke mix with water and pour over the top of the battery to remove the acid content created by over charging! once that is cleaned and removed then change your! plug wires too!!

1- For the overheat, remove the thermostat to run for a few days to see the problem come back. When the engine runs at iddle, press the upper hose connecting to the radiator to see there is a water flowing inside. a- IF there is then your water pump is OK. After a few days, put back the new thermostat to run as normal. b- IF there is not then you need to replace the water pump first.
2- For your battery draining. a- IF you change only the starter, then the solenoid is the culprit, not the battery, not the alternator. b- IF you have changed both then I suspect the diode in the starter and the battery. c- To determine which one is in item b, take off negative battery cable for 2 days, - if there is no problem when hooking back then alternator diode is a culprit. - if there is a problem when hooking back then the battery is a culprit. Good luck.

For the high rpm part, have you looked to see if there is a vacuum leakage or possibly a fault in the Idle Air Control motor.

With overheating since jeeps are single belt driven it could be possible the fan is starting up when driving slow or parked because the belt is moving right. Or look for leaks in the coolant maybe it's not getting enough coolant.

fluid in the glove box though, can you be more specific with that one.

idle air control motor?

weak fuel pump. clugged fuel filter. fouling out plugs.

You may have a loose battery cable,wiggle them both and make sure the battery clamps and associated wires are tight and not moving around.