feature of indifference curve
An indifference curve can touch the axes, take for example the case of perfect substitutes, if the consumer his utility is given by
 U=x1+x2
 then obviously he is indifferent between bundle (10,0) and (0,10). So not touching the axes is not a characteristic of indifference curves as such, even though in the case of Cobb-Douglas functions it holds.

As for your other concern, whether an indifference curve can take as input only one good, with the other input being money: this is perfectly possible, it is even a more general case than the indifference curve for two goods. In the case of the inputs x1= a good and m=money held by the consumer we can formalize the utility maximization problem in the following way: 
max U=u(x1,m)
Subject to the constraint: b=p1x1+m
As you see the standard form can be used with just one change: the price of a unit money held is of course 1.

And now the more general case, again let x1 be a good the consumtion of which we are interested in and now let y be the MONEY SPENT on all other goods. Now again we can use the modification of the budget constraint above. That is: price of y is 1. 
In short: anything can be an input in an utility function, just think about your own preferences: you dont just enjoy goods, you enjoy holding money and giving to charity etc. but also spending time with friends/family, with some modifications all this can be put in the form of a utility maximization problem and thus an indifference curve can be constructed for any two inputs, holding other inputs fixed.