Here's a couple articles to help you build some foundational knowledge:
To answer your specific questions:
I started to eat a lot and am wondering whether taking any protein products could be good for newbies like me.
Eat plenty, but protein products aren't really necessary. If you can get at least 1g/lb total body weight you won't be able to use all the extra protein. Since the supplements are expensive, save your money and buy a burger instead.
As a rough portion guide, a portion of just about any meat the size of a deck of cards (or your closed fist) is roughly 20g of protein. Give or take. Seafood has high protein and relatively low calories, while pork probably has the most calories per serving (and least amount of protein).
Just don't go too crazy. If you feel like you are eating a lot, but your body isn't changing, then do a little homework. Write down everything you eat. Maybe you aren't eating as much as you think! Also, quite possibly, you need to add more food. If you are gaining, you don't need to change anything until the gaining stops.
Also should I take a day off? I've worked out 2 days in a row. Heard overtraining could be bad for you.
I highly recommend you research some programs that are designed for beginners that have proven results. One off the top of my head would be Starting Strength. The book is a good primer on lifting in general, has some excellent tutorials on the main lifts, and will help you get reasonably strong in a short period of time. From there you can branch out. Just follow the program as it's written to help you get started.
By your question, you are so new to lifting that it's impossible for you to overtrain. It is possible to train almost every day even when you are an advanced lifter, but you have to be smart about it. You aren't going to be doing the big lifts every day.
The bottom line is that when you always feel fatigued, and you can't think straight, you've at least hit "overreaching". When you've hit that, then go light for a bit until you feel fresh again.