Can you worship a statue (idol) of Lord Shiva? Not just the Shiva linga.
Yes, one can worship an Image of Siva. This is discussed in Shiva Purana, Vidyesvarasamhita, Chapter 5. The answer is that the Saivites use the linga form to signify nameless and formless aspects of the deity and use the Image to signify Sakala Siva (Siva with name and form).
I am posting the quote:
Sages said:- 8. Everywhere the deities are worshipped only in their image. How is that Siva is worshipped both in the image and the linga?
Suta said:- 9. O sages, this question is holy and wondrous. Here the speaker is Siva Himself and not any ordinary person. 10. I shall tell you what Siva Himself had said and what I heard from my own preceptor. Siva alone is Niskala (nameless and formless) since He is identical with supreme Brahman. 11. He is also Sakala as He has an embodied form. He is both Sakala and Niskala. It is his Niskala aspect that the Linga is appropriate. 12-13. In the Sakala aspect the worship of His embodied form is appropriate. Since He has the Sakala and Niskala aspects He is worshipped both in the linga and in the embodied form by the people and is called the highest Brahman. Other deities, not being Brahman, have no Niskala aspect anywhere. 14. Hence the deities are not worshipped in the formless linga symbol. The other deities are both non-Brahman and individual souls. 15. In view of their being embodied alone they are worshipped solely in the bodily form. Sankara has Brahmatatva and the others Jivatva. 16. This has been explained in the meaning of the Pranava (Om), the essence of Vedanta, by Nandikesvara when asked by Sanatkumara, the intelligent son of Brahma, at the mountain Mandara.