First breath and regain some calm! As a parent we feel issues with sleeping, eating, behavior, etc will always last, but in reality most won't last. You're doing a permanent experiment on what's working and what's isn't, while the subject constantly change: it's really hard!

Eating in front of TV is bad for nutrition in general and especially bad for the kids, as multiple studies prove: almost no TV before 6 is a good rule of thumb.

As others comments are hinting, kids know how to regulate themselves regarding food intake, and no kid will let themselves starve, so you can offer a plate with the main course and a small dessert, your kid will eat the main course when she is hungry. Also we found that allowing them to come and go out of table was hard on our sense of properness but helped our kids to eat the complete dish. After a few months, there were able to stay at table for the duration. We also found out that industrial food for children is disgusting, and that nothing beats homemade to open the appetite!

Feeling (and being) overwhelmed is normal, if possible go see a professional to reassure you.

Sources: experience with my kids, reading a lot a studies, and a psychiatrist wife

Keep up!

Eating is tough with our 1 year old sometimes. What seems to help is not stressing about any particular meal and turning it into a struggle. If she doesn't want to eat much now, that's fine; she'll be hungry at the next meal or even the next day. Overall she gets enough and is gaining the right amount of weight, so it seems she's capable of regulating it herself, and we prevent pointless frustration for everyone by trying to force it. Of course if she wasn't gaining weight as she should be, it would be a different (and I'm sure much more challenging) story.