Nitrate leaching is obviously the main form of leaching due to the negative charge. However in very sandy soils I have seen with 15N tracer studies NH4+ leach if the cation exchange capacity is very low. The papers that I can think of on this topic are by I.R.P. Fillery, CSIRO Australia. He worked on very infertile, highly weathered sands (95-98% sand) with poor quality kalonitic clay (1-2%). I expect his papers are published in Australian J Soil Research (now called Soil Research).
The texture sand doesn't mean that sand represents 100% of the particle size distribution, clay and silt will also exist. This means that NO3- the anion can be easily leached from soil than NH4+the cation
Yes, it could if the colloidal particle of the soil is low (low CEC) and the amount of ammonium-nitrogen produced is more than the capacity of the soil to hold. For being a sandy soil, the probability of leaching is very high.
Though NO3 leaches easily, NH4 also leaches in light textured soils.
Pl. see ref: Prakasa Rao, E.V.S and R.Prasad (1980). Nitrogen leaching losses from conventional and new nitrogenous fertilizers in low-land rice culture. Plant Soil 57, 383 - 392.
It will also depend on the climatic conditions. Under humid climates and coarse textured soils, K leaching is definitely an issue. As chemistry of K+ and NH4+ resembles with each other, hence i believe it should also leach. But i have not seen any research reports so far.
Some tropical soils with low pH (acric character) can be positive charged and hold nitrate. It normally occurs in subsoil horizon where the low content of organic matter (negative charged) are at very low levels or absent and the clay particles are formed by iron and aluminum oxide and hydroxides. .