Answer: Although it is theoretically possible to grow tomatoes under lights, it is difficult. Remember that these plants prefer full sun outdoors and when grown indoors are usually in greenhouses for maximum sun. The plants themselves will tell you whether or not your lighting is both bright enough and of the needed spectrum to bloom and produce fruit successfully.
In terms of pot size, it is important not to move the plants abruptly in to a much larger pot than the one they are in. You might go from a three inch pot to a nominal gallon (actually much less than a gallon) to a two gallon and then maybe the five. If you transplant into a pot that is far too big, it is very difficult to avoid overwatering and the risk is that the roots will be in overly wet soil.
All the best with your project!
Q&A Library Searching Tips