If she is a Slovakian citizen, then she is part of the EEA, which means she gets to live and work in the UK. If you marry her, then you can come to the UK first with an EEA Family Permit. Once here, then you apply for an EEA residence card. As the spouse of an EEA citizen, you would (once your papers are all approved) have full rights to live and work in the UK.
The process for the EEA path is a bit easier than if she were a UK citizen (it is covered by treaty law rather than the ever changing UK law), and there are no application fees.
My husband is EEA so I know all about this and am happy to answer any questions about the process.
Overall though, take your time because changing countries is much harder than it seems at first glance. If she has had hard times in the past and they've been so hard that she feels she has to keep some big secrets, then she may still need some time to be sure about things. Everyone here will tell you that if it is meant to be, you will get there. It won't happen tomorrow, but it will happen. All the studies and qualifications you get will help you no matter what happens, so focus on that.