Can primary tumor cells grow in 2D culture?
Short answer: Yes, this is possible, it is the way most (cancer) cell lines have been generated.

Long answer: Culturing cells from tumor tissues is done in labs, especially, if you don't want to rely on the often very old cultures used in the labs. Many of these where started in the 1970s and are strange in many ways, e.g. contain many chromosomes multiple times. I have routinely isolated new cell lines from melanoma tissues (mostly metastases from different organs), but the general procedure is the same for other tumors as well.

To isolate cells from a tumor, you first wash the tumor sample to get rid of the blood. Then you cut down the tumors into small pieces using a scalpell, before adding a mix of enzymes like Collagenase, Dispase and Hyaluronidase to dissolve the tissue further in order to get a single cell solution. After the incubation with the enzymes the suspension is passed through a cell strainer to remove all remaining bigger cell aggregates and tissues residues and centrifuge the cells down. They are resuspended in an appropriate medium for the cell type and seeded to an appropriate plate/flask. For our samples this was typically either a 35mm plate (or a 6 well plate, which has the same area per well) or a T25 flask. Most cells from such isolations grow adherent, but sometimes you can observe cells, which do not adhere to the surfaces.

The procedure itself is not very complicated, but needs optimization. Depending on your tissue, the enzyme cocktail can be varied, as well as the length of incubation and the incubation time in this step. Then different plate/flask surfaces can play an important role, also the medium composition.

When we started doing this work in the lab, about 1 in 10 attempts was successfull, after optimization we went up to 6-7 of 10. What is important to take into account is, that the cells change during incubation and adapt to it. This means you need to question yourself, how good of a model they can be and need to be. If you need our detailed protocol, let me know, I can post it somewhere.