Can I extend my Schengen visa from Greece?
Mostly No. An extension is only granted under exceptional circumstances (such as serious illness) and requires the applicant to demonstrate availability of proof of funds. Source: Dutch government FAQ. For Greece a slightly out of date link is here. Quote from this link (emphasis mine)
Note that visa extensions are only granted under special extenuating
circumstances, such as being in the hospital, having a serious car
accident or a relative passing away. Visa extensions are not granted
because of ignorance regarding visas and permits, careless planning,
unexpectedly falling in love, taking illegal work and just because you
want to travel more.
Assuming your circumstances are exceptional, the procedure is also given in the same link
Visitors who plan to stay longer than the expiration date of a
Schengen or national visa while in Greece as a tourist, student or
temporary business consultant should apply for a visa extension at the
Alien’s Bureau Office or police station nearest their legal or
Apply between 7 to 25 days in advance of your visa’s expiration
For 15 days, you may not have enough time to even apply for an extension.
The other question:
What if I stay more than 15 days in my owns. Is not it that the Schengen visa is valid for 90 days?
I assume the
Duration of Stay on your Visa sticker says
15 and also has a time window given in
This means that you can enter Schengen area only ONCE and can stay only between the period mentioned in [
Until] (both days included). However, the total length of your stay cannot exceed 15 days because that is the number of days authorised to you in
Duration of Stay. The 90 days that you are referring to is the maximum duration permissible under Schengen short-stay visa.
If you stay for more than 15 days on your own, you will be breaking the rules of Visa issued to you by overstaying. Overstaying is a serious problem and can lead to many consequences such as fines upon exit, record in Visa Information System, problems in obtaining future visas and entry bans. In short, don't do it.
EDIT: For further reference,
this French Government Link explains the schengen visa sticker and what each field signifies.