2001 crown vic

hello im new to this site I just purchased a 2001 crown vic with 61000 miles on it a steal I only had it a wk and already having problems I done had to get a new altinator and battery installed in it and it shows my voltage gage is still low I had auto zone check it out and they told me the conectors to the altinator are bad if so could some one please inform me if this is the problem so I can get it fixed

id imaging it would probably be the connectors get your volt meter out

If the connector itself isn't making sufficient contact with the pins in the socket on the alternator, it could cause charging issues. You should be able to get a replacement plug(Motorcraft #WPT119) at a parts store, I know you can get one online, if you can solder then you can install it yourself.
If the charge wire is bad, you can replace it with a 4 gauge wire.
How is the belt?

the belts are in great condition and looks brand new ok now my battery light is lighting up in my dash board and I have not driven it for 2 days and when I started it up my battery gage show almost full

ok I just put new light bulbs for my dome light and they still not working what and how can I fix this problem