I think what's meant is that by putting it first, you can always treat any point in P^n as a point in P^m by just ignoring the extra numbers if m < n or by treating the missing numbers as all being 0 if m > n. That is the point in P^2, [1 x y], can also be regarded as the point [1 x] in P^1, the point [1 x y 0] in P^3, the point [1 x y 0 0] in P^4, etc. This is in contrast to putting it last, where if you have [x y 1] in P^2 and you want the point in P^1 you need to allocate a new list [x 1], etc.

The vector is sparse in the sense that you can regard a point as being an infinitely long list of numbers of which we are sparsely giving only that prefix that is non-zero (like how you can regard a decimal numeral as being an infinitely long list of digits, all the ones that are missing being 0).

[1] is the origin point in any dimension because it is [1] in P^0, [1 0] in P^1, [1 0 0] in P^2, etc.