Background chek

Hey everyone,

So basically i got a conditional offer from a bank until they do a background chek and I am a bit worried for some reason. So first of all I would like to say that I have an excellent credit score and that I have no criminal record.

1. My first question is will they contact my current employer? I don't want them to find out that I am looking for another job, I have a good relationship with them but I just don't want them to find out that I am looking to leave in case in dosen't work out or that they will fire me because of it. They seem to think that I will be staying there for at least another 6 month before moving on but I haven't signed anything with them and I am afraid of possible repercussion.
2. Some of my dates don't match. The reason why they don't match is because I have a shitty memory, I cannot remember the exact date I started or left a job and the same goes for education. Do they have acces to the governement data base to chek the dates or will they simply ask my former employers when I started and when I left ?

Am I in trouble ?

Thanks to anyone that will be awnsering my concerns !

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