What's the difference between a tempo and a tempi? At the start, how many tempo/tempi is White up? On average, how many tempo/tempi is one Pawn worth? What's the difference between a tempo and a tempi?
At the start, how many tempo/tempi is White up? Half, one, or two?
At the start of the game (before White has even made his first move), how many tempi is one Pawn worth?** (For players rated near ~2200 Elo.)
What's the difference between a tempo and a tempi?


Tempi is the plural of tempo. 


  At the start, how many tempo/tempi is White up? Half, one, or two?


At the start, White is not up any tempo. There is no such thing as a half tempo, because tempo refers to a single move from one side.  


  On average, how many tempo/tempi is one Pawn worth? 


This is hard to say. In open positions, often even 1 or 2 tempi might be enough compensation for a pawn and 3 to 4 tempi may make one's position better. In closed positions, tempi don't matter that much, so in those situations 3 to 4 or more tempi might compensate for the loss of a pawn. 

I'll give an example- 

Consider this opening - 

     [Event "2 Tempi gained by White"]
     [FEN ""]

     1. e4 c6 2. d4 d5 3. Nc3 dxe4 4. Nxe4 Bf5 5. Bd3 Qxd4 6. Nf3 Qd8


If you compare the position after Black's 4th move and Black's 6th move, Black hasn't changed its position; white has developed two extra pieces (2 tempi) and it's White's turn to move. However, White lost a pawn in the process. 

I analyzed this position with Houdini 1.5 at depth 20 and here's the assessment - 

After Black's 4th move - 

= (0.28): 5.Ng3 Bg6 6.Be2 e6 7.Nf3 Nd7 8.0-0 Bd6 9.c4 Ngf6...


After Black's 6th move - 

= (0.06): 7.Qe2 Nf6 8.0-0 Bxe4 9.Bxe4 Qc7 10.Rd1 Nbd7...


So, as per Houdini's evaluation White's two tempi was not sufficient compensation for the lost pawn (because the score reduced from 0.28 to 0.06. 

Now, suppose I give White an extra tempi, so that the following position is reached with White to play - 

 [FEN "rn1qkbnr/pp2pppp/2p5/5b2/4N3/3B1N2/PPP2PPP/R1BQ1RK1 w kq - 0 7"]
 [Event "3 Tempi for White"]  


Here, Houdini's evaluation at depth 20 is 

 +/= (0.54): 7.Qe2 Bxe4 8.Bxe4 Nd7 9.Bf4 e6 10.Rfd1 Ngf6 11.Ne5 Qb6...


So, Houdini thinks White is better with the 3 gained tempi after the loss of the pawn. 

Of course, this is just computer evaluation. From a human perspective, we can say that 3 of White's pieces are already developed and White is castled. Black has only one developed piece. None of it's kingside pieces have moved, so Black's king will be in the center for a while. White's rooks will quickly occupy the open files, so White will develop enough pressure. Thus, White is slightly better. 

In open positions, my judgment (subjective, of course) is that a pawn is worth somewhere between 2-3 tempi, whereas in closed positions, it may be worth between 3-4 tempi (if the side with the tempi uses the tempi to open up the position or gain a similar advantage). Thus on an "average", a pawn is worth 3 tempi.