EU has good developed production, so to grow economy up they need new markets and of course they need to protect their markets, because of that USA and EU controlls import to protect selfproduction. It is so easy to understand. And small country like yours will gain if EU will make business in your country.
I'm not quite sure what you are trying to say here. Yes, to increace economy, new market areas are usually searched, this mostly mean countries which are "stable". Good juridict system, transparency government and all in all no corruptions. These are very important parameters for economy and economic grow up. These are also the reasons why USA and EU are so dissapointed about Russia. Russia looked very promissing market area ~2000 - 2005 and new investors tried to do business in Russian and also offer better life for russians. Sadly, there was a military conflict 2008 with Georgia which caused some "alarms" for investors. Current conflict with Ukraine really vanished all investors from Russia. Sadly so, because there was a good start but nationalism won in Russia.
And about USA and EU control imports. Yes, there are tariffs for countries outside USA and EU area. But there are _also_ tariffs at Russian borders. That is the very reason why EU market area is so flexible, because the free trade. And this is the reason why so many ex-russian satelite countries' economy keep growing up in EU free market area. Those ex-satelite countries are great example how to offer better life for people and even some politics in Ukraine noticed this. They tried move toward west and EU and ofcourse, this isn't the diplomacy Russian leaders are looking for, right?
They will invest in your country money, make new places for workers. Export their products to yours.
Who are you referring with "they"? EU itself doesn't invest money if this will cause distortion in market. EU can invest money for new techology such as how to clean pollution or less energy consume engines and such. You see why this desires companies to invest EU and drag new brainstorm? This creates new jobs for workers but also helps companies to find cheaper (read: correct market value) employees. For example, there are huge number of Estonian workers in Finland. Finnish companies can offer they server cheaper, offer also jobs for finnish people because they can compete on price, it's a win-win-situation for people and country (tax money).