modification due to going concern issues

The first one is correct. If the note about going concern worries is omitted, it is more likely that there would be a qualified opinion. It would be unusual to give an adverse opinion just because a note was missing. If teh auditors feel that there is no realistic chance of the company continuing then the FS should not be drawn up on the going concern basis. If they were drawn up on the GC basis, then an adverse opinion would be expected because the FS are fundamentally flawed.

Threat arising from an inappropriately close buisness relationship with a client is it familiarity or self interest threat?

Threats can be multi-faceted. For example, if the older brother of an auditor was the CEO of an audit client, threats could be: Familiarity Self-interest to avoid a family row Intimidation because when kids he used to beat you up and some fear still lingers. Your question depends on what is meant by 'business relationship'.