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@andreactamayo wrote:

The first one is from a foreign company located in Slovakia.

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Was your client on secondment from the US to Slovakia, at least as far as the local employment is concerned?

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The second is from a self- employed job with clients located in US.  

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Tax question aside, what kind of visa is your client on in Slovakia?  Employment visas typically do not legally permit side gigs.

Also, regardless on whether immigration regulations may have been breached, such self-employment income should be subject to Slovakian tax.  Is your client paying tax locally for this income?

Another related question: What type of entity structure is your client operating this business under?  Have you considered the US tax classification of this entity and the related US tax implications as well as information reporting obligation?

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I would like to make sure that his self-employment income has to pay Social Security taxes in US due to that this income is not consider a foreign source of income.

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Where one pays social security tax under a totalization agreement is not determined by the sourcing of income but based on territorial and detached worker rules.  If these are not familiar terms, you would want to do some research.

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Can his services be consider performed in US while he is living abroad ? 

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No