My questions are:
Q1 How reliable are these reports? If I'm getting a report about 6-7 ships spotted, can I be 100% sure that at least 1 Eship is in the area?
This is called "FOW" (Fog of War). Your Recons are most likely reporting your own ships as hostiles ones. Especially at the outbreak of the war, when your crews are unexperienced, this will happen quite often. Serious sighting reports will show an anamy TF symbol on the map when the turn is completed. Anything else has to be viewed with all due reservation.
Q2 If the answer to Q1 is that the report is not always reliable, is there any realistic explaination on why someone would report 6 ships when there are none?
Yeah, because the recon has falsly reported own ships as hostiles, has greatly overexaggerated the number of ships, or made ofther mistakes.
Q3 If I'm especially worried about a report and want more information, is there anything I can do besides sending Naval Search and subs?
ASW Patrols (both air and naval) to detect subs, naval search missions to spot enemy TFs. But You should learn to live with about 30-50% false or misleading reports. C´est la guerre :).