Are Tommen Lannister and Myrcella Lannister offspring from the (incestuous) relationship of Jaime and Cersei Lannister as well?
Yes, they are. In the novels, this is made very clear, though it's possible they've glossed over it on the show and I didn't notice (knowing the truth already I didn't pay much attention during that bit).
Near the end of Game of Thrones (staring around chapter 40-ish), Ned is trying to retrace Jon Arryn's investigation that he suspects got him killed. He eventually comes across a book that describes all of the highborn children dating back many, many generations. According to the genealogy book, in every case where a Baratheon father had a child with a Lannister mother, they always favored their father very strongly - broad shouldered and dark haired (e.g. like Gendry). Later on, when Sansa remarks that Joffrey will father lovely golden-haired children for her, Ned finally connects the dots: all three of the Baratheon children are described exactly the same way, and those characteristics are those of Cersei and Jaime.
Later on, when Ned confronts Cersei about his discovery, he includes all three of her children in his accusations, and Cersei doesn't deny it.
Depends on which question you're asking.
Are Tommen and Myrcella the result of incest? Yes, as answered above.
Are Tomman and Myrcella bastards? No, or at least not known as such. Their parentage is officially that of Robert Barratheon / Cersei nee Lannister. As such, and until such time as they are "officially" (probably as a result of clerical finding) exposed, they are not bastards. Under British law, which seems the appropriate framework, bastardy has to be established, either by common knowledge or by jury trial. This is actually a somewhat tricky question, along the lines of "does a tree falling in the forest make a noise if no one hears it?". However, in this context bastardy is a legal term, so until a legal determination is made the label does not apply. And so far, both in the books and the show, no such determination has been made.