Hi, I have some experience here so let me try answer your questions.

If she's been denied entry, they will put her on the next available plane back to her country of origin. Generally this will be her source airport, but it can be almost anywhere in the US, so she may be sent back to New York or such like. The alternative here will be a detention centre somewhere in the UK. If she's got any sense at all, she will take whatever the first plane is. Don't let her go to the detention centre, they are extremely depressing and miserable places.

It's important to note:

• She's not under arrest
• She hasn't committed a crime
• There is absolutely nothing she can do about this decision. Tell her not to get outwardly mad/angry/upset as it will only make the situation worse.

When she is given her departure details, the customs officials will explain very clearly what the circumstances are, and it will vary based on circumstances. She needs to ask the following questions and write them down to be sure

• What is the reason I was denied permisson?
• Do I need a particularly visa on my next visit to the UK?
• How long is it before I can apply for a visa to re-enter the UK?
• Ask for some documentation showing my reason for not being allowed to enter (this is really useful when applying for a visa, so be firm on this, it's part of the denial process but some people aren't given it)

Regarding your trip to the USA, it's a difficult situation. USA immigration can be just as difficult as the UK immigration for us brits. Here's some rules I tend to follow when I was heading to the US to visit my now wife.

• Book trips of a reasonable length. Long trips like 6 weeks will be heavily scrutinised by officials
• Have your return flight details memorised and readily available
• Have an itinerary, or a list of things you're going to do, like a true tourist would. People who are visiting who don't know what they're going to do are extremely suspicious looking
• If you're visiting the US for the first time, it's important to say you're visiting friends, and not a girlfriend/boyfriend. The official will ask where you're staying and the nature of your visit - if you say you're staying with a friend it'll give you an easier ride, but don't outright lie to the official. If they ask you flat out if there's any romantic interest between you two, you should be as honest as possible, but don't make it out like you're exclusive boyfriend and girlfriend because to many people, a LDR is not a proper relationship. Usually on my first few visits I would say "I'm staying with a friend" and it would be enough. They occasionally asked if it was a romantic friend and I would say "I hope so" and they were fine with that, as long as I was going home.

I'm sorry this has happened to you, advise beforehand from this subreddit would have helped a lot. All hope is not lost for the relationship, but your partner will probably need to apply for a visa before her next visit to the UK.