Is this good?

What is the state of this?

Move 3 violation of opening principles, so better for white. White can play d4 and have a nice position. Nothing completely lost just yet though, but nice for white.

Can white seize a tempo advantage?

White has an advantage

Well 3. ...a5 is giving away a tempo. Since white may start, he is always up a tempo, but now 2. The question is whether he can make the tempo count. The thing is, in e4-e5 structures that is harder than it might seem. For example, moving ..a5 is a possible line in quite a few Italians (with Bc4) and Ruy Lopez (with Bb5). That's why I'm suggesting 4. d4. This hopefully will open up the position, where you can take advantage of the tempo black lost. 

But it's difficult stuff to take advantage of an advantage in time. If you just keep developing, you'll get a reasonable position too. And if your opponent makes some more unnecessary pawn moves, you'll easily get a big advantage if you just make sure that you develop all of your pieces and then open up the position with a pawn break.

What type of advantage?

What counts as an unnecessary pawn move?

Any pawn move that is not aimed to control the center. So ...h6, ...a5 etc. Basically any pawn move costs time that you could spend on developing your pieces. It usually isn't worth the time to spend a pawn move that doesn't aim to control the center. And even then too many pawn moves can be very bad. 

After 4.d4 the only possible move for black is to go 4... exd4 otherwise black loses material. I looked through the next subsequent moves for the alternatives and none of them seem to be good,

4 c3 to prepare 4 d4 should be enough to win for white: he gets a solid control over the center.

4c3 and 4d4? White gets to move twice in one move, definitely winning.

I don't understand the plan with 3. - a5

White can continue with 4. c3 and if 4. - Nf6 5. Ng5!

How is this bad?

Any move not winning material but still winning the game on move 4 had better be checkmate, otherwise I'm not buying it. 

Also I disagree that 4. c3 and then 5. d4 is winning at all. In fact, I've chosen 4. d4 because I think 4. c3 is not good enough.

I think 4. c3 should be strong. Black can't play 4. - Nf6 to counterattack the centre so there is no way to prevent 5. d4 giving white a strong centre.

 A position can still be completely lost due to having no compensation against an opponent with great advantages.

Is being a tempo down losing?

No, but it's a disadvantage.

Is there a way to make the disadvantage worse?