Does the prohibition of Kilayim for fruits, vegetables, grains and herbs, etc… apply to Chutz LaAretz? Am I allowed to plant seeds of the above in close proximity to each other, here in my garden/backyard in North America? Thank you.
Kilayim applies in chut laaretz in a limited form. Essentially there are three different types of kilayim, klayim of trees, kilayim of vineyards, and kilayim of seeds. In Chutz Laaretzone may plant different seeds of different vegetables in close proximity to each other and it is fine. The seeds may even be planted next to trees, but not near a grapevine. It is also prohibited to graft the brach of one tree to another even in Chut Laaretz.
Rambam Hilchos Kilayim 1-5, Y:D 295-1, 3 296-1,3 297-2.