The heater core may be plugged. After the vehicle is warmed up to operating temperature, feel both hoses (careful they may be hot) and see if they feel equally warm. If one is noticeably warmer than the other, your heater core is likely plugged.
Do you have the luxury model ? The ticking you hear is probably the Turn/Hazard Flasher
Mounted to the convenience center, under the left side of the IP, to the left side of the steering column, on the bulkhead .
Is this about where you hear the ticking ?
How good of battery did you buy ? A cheap one from walmart ? They won't last long ,they are junk . The only way the alternator would kill a battery is by over charging , you would need to hook up a voltmeter to the battery an see how much it's charging . 15 volts or over is too much . Do any of light's flicker ? Could be a bad diode in the alternator . You can take it to most auto part stores an they will check the charging system free .
Does the vehicle have these ?
/Daytime Running Lights (DRL)
The high beam problem i would suspect the switch ,but without testing that would be just a guess .
I would venture to guess you have no clue on how to do automotive electrical circuit testing . Looking at wiring diagrams for the problem circuits an testing with a DVOM - digital volt ohm meter is the correct way to find electrical problems . Not thinking it's this or that or guessing . I would suggest that you have a qualified repair shop diagnose the problems. Free wiring diagrams here http://www.bbbind.com/free_tsb.html Enter vehicle info. year , make , model and engine . Under system click on lighting ,then headlamps .Click the search button then the blue links .
Watch these videos Electric Testing Techniques You Need to Know
GM used different anti theft systems if your key wasn't programed. You need to look up how to program your keys. There are also working fixes to disable this. I just got a 05 Buick without a programed key and has the wiring fix. I can't get the key to program for my car but I may have done the wrong programing.
You may have plugged the filter. The fuel pump may have gone bad from the empty tank. You my have not ran out of gas, but assumed you did because the fuel pump quit.You may want to have the pressure tested.