Some kids do great with “grazing”, and others respond better to set meal times at the table. Adults, too, for that matter. Since it looks like grazing doesn’t work well for her, maybe try fixed meal times - beginning and end. Present the food, look at her expectantly while you eat a snack, then when you’re done, clear the table. No more food until the next predetermined meal time. You’re right - don’t be upset, don’t beg or cajole or force, just present the option, provide an example and clear the table when meal time is over. That may help train her belly to expect food (ie, be hungry) at regular times, and will help socialize her to eat when the food is presented, not when she gets around to it. These “meals” may be all of 5 minutes, but getting into a routine may be what the doctor…uh…didn’t order. 
Self soothing for sleep is a whole can of debate. Some parents don’t subscribe to it at all, and maintain that it’s best to have constant contact for best sleep. Some parents do a literal “cry it out” where they just ignore the baby until she exhausts herself back to sleep. I know of exactly zero research on risks or benefits of either method. It really seems to be about equal in outcome, and up to parental preference and parenting philosophy.
I’m in the middle. Here’s how I did it with my kids:
Establish a solid bedtime routine, one that’s short and simple enough that you can do it at home, at grandma’s, in a hotel room or in a tent. Wherever Baby goes, so goes the bedtime routine.
Brush teeth (soft washcloth on the gums if they’re not using a toothbrush yet).
Wash face and hands.
Read a book together.
Sing a good night song. (We used the “We love you Conrad” song from Bye, Bye Birdie, with “Caileigh” in place of “Conrad”) This song is *only *sung at bedtime.
Get kiddo into bed.
Turn on the night light.
Tuck in and kisses.
“Good night!”
Turn off room light.
Blow a kiss.
Close door.
That routine is still going strong in our house, and she’s 8. That song is like a Pavlovian switch, I swear! The first few notes and her eyes start to droop! In fact, there was a time when she was about 5 or 6 when she started asking us not to sing (parents are so embarrassing to kindergartners sometimes!) and we’d hear her singing the song to *herself *after we closed the door! 
So, then she’s going to wake up in the middle of the night. Now what? Again, here’s what we did:
Open the door, walk in quietly (do not turn on the light).
Reach into the crib, pat her on the back, pull the blanket up and whisper, “Shh…still sleepy time…”
No eye contact, no picking up, no toys, no boob. Keep it as boring as possible.
Wait until she settles and then move to the door. She will probably stir again and may cry.
Stay where you are and softly say, “Shh…you’re okay…still sleepy time.” Wait until she settles again. Scoot out the door.
This is where the cry-it-out, modified, comes in. When she started crying again, we gave it 2 minutes. 2 timed with a clock, very long minutes, standing outside her door feeling like the worst mom in the world. Then repeated the above, gong in with as little stimulation as possible and quiet soothing.
Then 5 minutes to cry. Then 10. Excruciating. (For us, not her.) If she cries again after the 10 minute round, give up for tonight and try again tomorrow. I personally think a baby crying for more than 10 minutes has gotten herself so worked up that she really can’t bring herself back to calm well.
We only made it to 10 the first night. The second night, she settled after 5. The third night, after 2. There was no fourth night, she just slept like a normal human being.
I’ve done the same with several kids of various ages youngest was 10 weeks from her due date (my daughter), oldest was 6 years old! (Older kids I do 5, 10 and 15 minute rounds.) Some I was nannying for or helping the parent with an intervention of sorts. It’s hard on the parents, I won’t lie. But the kids seem uniformly relieved.
