She sounds normal! All my kids went through what you're describe around 1-2 years old. My son was the worst... there were days I had no idea how he was functioning - he'd literally go an entire day eating 5-6 bites of food! But guess what? He's 7 now and eats pretty much anything you put in front of him.
Don't cater, don't become a short-order cook. Kids will not starve themselves if they are presented with a wide variety of healthy food. Your job as parent is to prepare and present the food, it's your child's job to actually eat it. Don't start a power struggle - you won't win. No matter what you do, you can not force a child to eat (you can threaten, remove other privileges and punish but in the end, if the child chooses to accept those other things, they won't eat). Put the food on her plate, set it in front of her and turn your attention to other things. By the 1st birthday, a child should be eating whatever the rest of the family is eating - just cut into pea-size bits to make it easier, especially if she doesn't have teeth yet. We do have the 10 minute rule in our house for 1-2 year olds - they have to sit at the table for 10 minutes (trust me, that seems like a lifetime for an active toddler!). We talk about anything except food at the table. The more the food is talked about, the more they resist eating and try to get into a power struggle. When the meal is done, the plate goes away. If they didn't eat, oh well... they are hungry until the next scheduled snack/meal time.
A few tidbits... toddlers' tummies are small and they need to eat snacks between meals. Make them healthy. Don't skip them - a very hungry child is more prone to tantrums and meltdowns.
Green veggies taste bitter... just like poisonous plants. Through evolution, kids' tastebuds are very sensitive to bitter tastes -- probably to keep them from eating bad plants as they roamed through the woods.
Eventually they'll try new foods but it can sometimes take 20-30 or more times. If you hide veggies, be sure to put a piece of the veggie on the plate, too, so they can see it and maybe even eventually eat it.
A 1 year old simply needs MUCH fewer calories than a baby. Your baby tripled (or more) in size/weight the first year. A toddler only grows a few inches/pounds during a year. A serving size for a 1 year old is a tablespoon so a small pile of green beans is enough for the day. Think of the picture... write down what she eats over the course of a week -- it more than likely all balances out and she's getting what she needs.
There are days when a toddler will eat literally 4-5 bites of food. There are days when a toddler eats adult-size portions at all meals. There's no pattern... just go with the flow.