I have advertisements displayed on my site, which is a shopping company. Should I remove them from my site before I apply for Google AdSense, because I don't know if there will be any implications if they are left there.
I've used adsense before and they don't require that they become your only source of ads. Having said that, you still have to follow their content rules and that includes ads. If you have content that is against their policies like adult content or hate related information among others, they will cancel your account. I'm sure that if you have ads that go to sites with the same type of content they will take the same measures. If you just have ads to a regular shopping site then you might be fine.
Here are the AdSense program policies. https://support.google.com/adsense/answer/48182