Well, the GDPR doesn't apply to "a natural person in the course of a purely personal or household activity", so they can upload them, assuming they're personal contacts.

For contacts of clients and such, probably yes, since whatever conditions for allowing their processing in Gmail probably also apply to Skype (and vice-versa). But it might not if for some reason the other service offers less security or control over that data.

That makes sense from the uploader side. But can the service store and use data about me because you uploaded it? In this case I have only added my data to Gmail, and never allowed Skype to have it and have not accepted the terms from Skype.

Maybe. It can probably use this to help the user who uploaded it do something, since for that purpose it's evidently suitable - if I upload the claim that rypskar has the nickname "Dog boy", their phone number is +1-555-555-1234 but they live in New Zealand, then providing that information back to me seems pretty harmless even if it is bogus.

But if they take this data and then try to do something else with it, whether that's contact rypskar or give the data about rypskar to somebody else - that's going to run into lots of GDPR problems around correctness (the data processor is obliged to take reasonable steps to ensure the data is accurate and fix problems on request) and as you identified with permissions (did rypskar authorise this? How do we know? Who even is rypskar?)