Well it is unlawful to have a 'relationship' in islam, but seeing that a guy and girl met, and can't afford to live together as yet, is it ok to nikah and live apart, so as to make the relations lawful, until they can further afford to live together.
Do you know what is the differnce between arab engagements and asian engagements?
Asian ones are the same as the kuffar ones. You propose, slap on a ring and you are engaged. You can spend some time to better get to know each other, but you are still non-mahrams and still have to adhere to all islamic rulings.
Arab engagements are the nikkah without the see off. Basically you do the nikkah and then you can date each other, spend time together, go out, get to know each other. And all of it is halaal because your "engagement" is the nikkah thus making you lawful for each other islamically. So when they feel comfortable and know each other enough, they get "married", this marriage is where they do the see off and the girl goes to the guy's house to live together.
So in other words, what you are asking about is the arab engagement and is allowed and better way to go bout it. As for the 2nd part of that question...
Many Muslims are doing that in the arab world now and maybe other parts of the world. They do nikkah and have relationship with each other but don't live together since the guy can't afford it yet. So he visits her at her parents house and spends time with her. Technically it is halaal but something scholars frown upon and advise against. When you marry and move in together, you learn to adjust to each other, to take on responsibility, to work together as a family. When the guy comes to you and then goes off again doing his business. Then this sacred bond of marriage is reduced to nothing more than a bf/gf relationship. He gets to enjoy his single life without any responsibility and he can go to the girl whenever he wants. This in longer time can actually damage the relationship. The two don't learn responsibility and commitment and other things that come with living as a family. It weakens the family values they would normally be building.
So i'm for the nikkah and getting to know each other, but i personally would advise against conjugal relations type of relationship as a bad idea for long term. It's good to do nikkah but better to not wait too long before moving in together as a family.
i believe you can find similar question at islamqa.com