As for TV, I usually sit with my 5 year old son if he is watching tv. We usually sit together on the sofa and it is our snuggly time. He doesn't watch tv every day, but I will let him watch up to 40 minutes a day sometimes. Or once or twice a month we will watch a movie, longer documentary, or sports.
I have found that he sometimes gets scared, even of the cartoons; even something like Winnie the Pooh can somtimes scare a small child. When he was 3, being with him was better. I could turn it off if I noticed he was scared. Now at 5, he is better at turning his head and telling me that he doesn't want to watch something anymore when he feels scared.
I usually use the shows he watches as a way to develop his language and creativity. I have him tell me the story. (Even at 3 years old, I had my son try to retell the story. Watching it with him allowed me to fill in the blanks and help him find his words better. ) We talk about how the characters behavior was good or bad. I have him imagine what might have happened next in the story. I encouraged him to role play the story when I thought the lesson being taught could help him. I also encouraged him to draw pictures about the story and characters, either retelling what happened in the show or being creative and deciding what happened next in the story. When I started teaching my son to write sentences, the stories he watched on tv became a good source for his writing. There are many ways to use tv watching as a learning experience.
That being said, I don't spend every minute of the day engaged with doing something together with my son. I might be in the same room, or a room away but still able to keep an eye/ear on him. At 3 years old, I started encouraging my son to have short independent play times where I could read a book, check my e-mail, start a load of laundry, etc...
Now at 5 years old, I will still watch a show with my son if it is the first time he sees it. If it is a repeat that I know he doesn't have any problems watching than I will sometimes do my own thing. I still like having snuggly time together so I will sometimes sit and watch a repeat too.
Don't feel guilty about taking a few minutes of time for yourself. You are important too! If allowing your daughter to watch a few minutes of tv is the only way for you to get that free time for now, then take it. I would like to recommend that you find a way to teach her to play independently as well though so you don't have to feel like you are sneaking away from her. Maybe you can let her look at books while you check email or have her sit at the kitchen table and draw pictures while you cook dinner. Then you will both be doing your own thing, but she will be where you can keep and eye/ear on her. I use music or a timer as a way to help my son know when our independent time is finished. If I am having him play with something in his room or the living room while I am taking care of laundry or cleaning the bathroom, I will put in one of his CDs or set a timer for him to clean up when it ends or beeps.