Very beginner question

Hello, I just played a match a few minutes ago with black.

White started with e4

I played d5

He played e5

I played Nc6

He played d4

Here, I felt I was not in a good position ?

My questions are :

Q1 - Is it an acceptable start for black ?

Q2 - If no, what should I play after white played e5 ?

Q3 - Is there a place where I can figure out by myself the answer of my questions Q1 and Q2 without having to post a forum question ?

Since these are very basic questions about the 4 first moves, I expect to be able to find answer without paying a fee or buying a book. I am looking for extremely basic information about the very very begining. Does such very-beginner information exist ?

Right now, I really have no idea of the anwers of my Q1, Q2 and Q3. I kind of feel that I was not in good position after white played d4, but, I am certainly wrong ...

Q1 yes Q3 There's an opening Explorer database on site, but it's a premium feature.  I bet if you googled something like "free chess database", you'd find something though.  Or of course you could bump up your membership to premium...

Just to give you an idea of what the Explorer does:

Q1: At the beginner level yes. You put a pawn in the center and developed a minor piece, so that's very reasonable.

Q2: After 1.e4 d5 2.e5 white will want to support his far advanced pawn by moving d4 so it's better not to block your c pawn with the knight. Nc6 is a good move, but it's better for you to play c5 first. Black wants to play c5 because it will attack d4.

Q3:  Engines are free. You can also use chess.com:
https://www.chess.com/analysis

The opening explorer is free up to white's 4th move, so he could use it for this question.

https://www.chess.com/explorer

I did not know that...

I'm lucky I'm a free member otherwise I wouldn't have been able to test it

To answer the OP:

1.e4 d5

This move is "ok" but 1...e5, 1...c5, 1...e6, and 1...c6 are all stronger!

2.e5

A bad move.  White should take on d5.

2...Nc6

Take advantage of White's mistake and play 2..c5 and 3...Bf5.  You get a Caro-Kann a tempo up (one move to play c7-c5 like the French, but with the Bishop outside)

3.d4

Now White has put you in an inferior opening, The Nimzowitsch Defense, normally reached via 1.e4 Nc6 2.d4 d5 3.e5.

I must say I do not want to pay for premium feature while I played only a dozen matches of chess in my whole life. That said, I understand my answers can be found using the https://www.chess.com/analysis tool. So, I have to figure out how to use it.

To start, I will try using the tool to figure out what ThrillerFan said :

1.e4 d5

This move is "ok" but 1...e5, 1...c5, 1...e6, and 1...c6 are all stronger! <= This is very valuable info

2.e5

A bad move.  White should take on d5. <= Again, this is a very important information I hope to be able to figure out by myself using the analysis tool

Thanks everybody for your answers.

I am not sure what I see in the tool https://www.chess.com/analysis

After white played it's first move e4, it seems the best answer for black is Na6, with 77% win for black and only 15% for white.

Did I use the tool properly ? Is it how I can learn the very first moves ?

Since there are only 13 games for Na6 you can ignore the stats.

Also, if you click on Na6 to see how the next few moves go it's not looking so good for black anymore...
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Also, since you're new, please ignore most opening names... it's as if programmers go nuts wanting to give every terrible variation a name.

No one has ever heard of the De Bruycker Defense. Most people would call this "my opponent played some Na6 garbage."

First you need to learn to write chess notation 1.e4 d5 2.e5 Nc6 3.d4, then you need to understand why the moves are made and what they are doing to that end 'Logical Chess move by move (every move explained)' is an excellent book by the well respected Irving Chernev.

Here's a recent Grand Master game that opens similar albeit a different move order

lichess.org has somewhat simpler database for openings. And it's free. 

I did not realize there is a count of games in front of each proposed move. I think I can find my way with that.

Thanks Everybody.

Openings are not important. You are rated 566. What matters is to not hang too many pieces. And when your opponent hangs a piece, just take it.