If I buy iPhone on Apple.com (I’m from Russia), Does it will be work in USA?

If it is unlocked and SIM Free it will work anywhere in the world. I buy from the USA and use them in India with the local carriers.

All iPhone models are world phones, so you can use them almost anywhere. Whether you are a GSM or CDMA network customer, you can roam internationally on GSM networks in over 200 countries or regions around the world. Availabilitys of LTE data varies in some countries or regions and depends on carrier support for certain LTE radio frequencies. Contact your wireless carrier for more information regarding international roaming policies and rates.

If it's unlocked (either new or after the carrier unlocks it) you shouldn't have a problem. But if you buy it locked to a specific carrier then it's not going to work with any other carrier unless you get it unlocked. It typically depends on how you got your phone and if there's a subsidy where you signed a contract to have their service for a required amount of time. It may be different in Russia, but I'm guessing it not.

And if it's still locked, it might only be possible to use it in the USA under whatever roaming fees are charged by a Russian cellular carrier. Unless there's a specific plan that includes US use it can be expensive. For example, I've got a plan in the US that covers use in Canada without any additional fees provided my data use for the monthly billing cycle is less than 50% in Canada)

I've known people who had iPhones that were brought to other countries and worked. But they were either purchase unlocked, or the contract was completed and the carrier unlocked it.