ASUS N61VG Laptop -- Battery, RAM, and HD Upgrade

Hello. I just had a question with regards to my ASUS N61VG laptop ( ASUSTeK Computer Inc. - Notebooks- ASUS N61Vg ).

So recently, I was able to get some extra money, and I was hoping to kind of upgrade my laptop parts a bit (everything in my laptop is all factory parts, and I have not got the chance to buy anything like new RAM or a new HD or anything for it yet).

Firstly, I was hoping to get a new hard drive for my laptop. I was hoping to get a new hard drive with at least 1 TB on it. Is there a specific one I need to get for this laptop? Or do you guys have anything you would recommend me from anywhere (hopefully Amazon since I have amazon prime lol). Around how much would a good/decent one cost? Links?

Secondly, I was also hoping to upgrade the RAM for my laptop. I also have the one that came with it (specs of the laptop are in the link above), so is there a better one you guys would recommend me to get that would work for my laptop that can enhance the laptop performance of my laptop? Around how much would a good/decent one of those cost too? Links?

Lastly, I have one last problem. Also, recently, for some reason, whenever I unplug my computer from its charger, the computer shuts off. I think its because for some reason, the battery drains out right away. Does this mean I have to get a new battery? If so, is there a specific one I need to get? Or, do you guys have anything you recommend me to get? Again (sorry if I keep asking this), but how much would a good/decent one of those cost too? Links?

Thank you so much for all of your help in advance!