What's wrong with my 2000 ford contour? Alternator?

I have a 2000 ford contour sport SE V6 and I've kinda always had problems with it. I've had problems with the battery draining the past year but I just unplug the battery now everytime I'm not using it. Anyway, I think my alternator has always been bad but I'm just wondering if this is what's actually wrong with it now. Tonight I left my battery plugged in just cuz it was only 30 mins til id be driving it again (which it never dies that fast) but it was dead when I went back to it. Which is weird. An it was barelyyy dead, so it jumped easily and fast. Anyway, when it was started the dash lights were VERY dim and I think my headlights were also dim but i couldn't tell and forgot to look when I got out. But it drove fine for about 2 blocks then the last 5 blocks it started acting like it didn't want to go when I pushed the accelerator. It almost felt like I was running out of gas cuz it wouldn't want to go but then it would go for a few seconds then the accelerator would kind of stop working again. Very weird. I know it wasn't gas cuz I had a half tank. But does anyone know what this could be? Is it my alternator going out? Any other suggestions? If it is my alternator, do you know around how much that costs to fix? (Without labor fees) just the price of getting a new one. 11 pts to best answer and thank you so much! I need a good answer as I'm 35 weeks pregnant an I don't want to be driving this with my daughter if something is majorly wrong.

Find a shop to test the starting and charging systems. Either or both will be a factor.

You have a system that is still on. It is draining the battery. There may be nothing wrong with the alternator.
do you have a test light? Its an inexpensive tool. Remove negative battery lead and connect test light to battery and the other end to battery cable. Is light on? You have a draw on the battery. Pull fuses one at a time until light goes out. Find out what systems are on that fuse. Reconnect fuse and disconnect power to those respective systems one at a time until light goes out. You just found what system now you need to find out why. By the way if you leave the door open it dome light lights your light so you need to depress the door switch or turn off dome light.

Take it to autozone or another auto part store. They will often test your alternator for free too check it. It sounds like you have some electrical short or leech going on with the system as well.