I work on a project in Europe, but most of the time from my home in the US with occasional trips to the Site. I am employed by an agency in Europe on hourly rate basis and paid from Europe to my US bank account. I am not claiming foreign residence or income deduction. I am a permanent resident of the USA. Question: Am I liable for paying self-employment tax under the circumstances ?

of course. As a US resident( a green card holder), you are subject to US taxes, federal/state, on your US source and world wide income; so perhaps you need to pay quarterly estimated taxes on your self employer income. As you need to pay taxes to the foreign taxing authority(ies), you may claim taxes paid to the foreign taxing authority on your US return as foreign tax deduction on 1040 line 47 y filing form 1116 or foreign tax credit on Sch A of 1040 line 8. If you are filing as a sole proprietor and/or a self-employed individual, you generally have to make estimated tax payments if you expect to owe tax of $1K or more when you file your return;however, you do not have to pay estimated tax for the current year if you had no tax liability for the prior year
;You were a U.S. citizen or resident for the whole year
;Your prior tax year covered a 12 month period.

Question only related to social security (self-employment tax). Since I am employed outside the US and income is earned at a foreign project, although not claiming a foreign tax home, do I declare and pay the approx. 15% soc. sec. / self-employment tax?

as said it depends;aslongas the number on sch se line 2/ 3 is $400 or exceeds $400, then, you need to pay seca tax and deduct 50% of it when you file your return on line 27 on 1040.