Hi Alison! First of all, congrats on finally having that precious little baby!
I have an 18th month old and another one on the way in May, so I know what you're going through - it can be so confusing! I'm certainly no expert, but I'll tell you what I do know and what I've learned from experience:
Regarding feeding...
--She should be taking a ballpark of 40oz of formula per day to meet her nutritional needs, and a 6 to 8 oz bottle is pretty normal. Other than that, if she's drastically reduced her intake I'd talk to her pediatrician about it...
Regarding sleeping (and just to let you know, I was obsessed with helping my son become a good sleeper!)...
--The fussiness between 4p-8p sounds like a baby who is over-tired to me. Most babies still take three naps at her age, and the third nap of the day is often a catnap in the late afternoon.
--What time are you putting her to bed? Sometime between 6pm and 8pm is the best time for a baby that young to be going to bed. My son went to bed at 6:30, and gradually went to bed later and later. He now sleeps from 7:30p-7:30a w/out a peep. Prior to that it was more like 6:30p-7a. He often took a 20-30 minute catnap around 5pm, too. I usually had to hold him to get him to nap at this point, though.
--Do you have a solid bedtime routine in place? For instance: Bottle, followed by bathtime, reading a book, and putting her down in her crib drowsy but awake... We travel a lot and keeping the bedtime routine the same no matter where we go has REALLY helped him sleep well wherever he is.
--Until he was seven months old, we gave him a "dream feed" at 10pm. We went into his room, kept the lights off and gently took him out of his crib and fed him a bottle while he was still partially asleep. He often took the whole bottle - it may or may not have helped him sleep through the night, but regardless of whether it did or didn't help him sleep all night, it did help him meet that 40oz/day of formula.
--For naps, I followed up a bottle with a book, and at 4 months I was still swaddling him in a Swaddle Me blanket for naps and bedtime. Naps are tricky at this age - babies are notorious for getting bitten by the "15 minute nap monster" and sometimes won't nap well at ALL. She should still have a morning nap about two hours after she wakes, and then an afternoon nap about another two or three hours after the morning nap ends. Watch for the early signs of tiredness - eye rubbing, yawning, looking away from you or a toy...
--IF you are comfortable letting her cry, then DO IT. Start with five or ten minutes. If she wakes up after only sleeping for 15 or 20 minutes, let her cry for a few minutes. She might surprise you and fall back to sleep for another hour.... my son often did that, and they really need that sleep to allow their brain to develop. I know that letting a baby "cry it out" is controversial for some and a personal preference, but it worked well for me. Four months is the age where habits begin to form, and I felt that if I consistently rewarded my son's cries by immediately attending to him, he would always cry to get the attention he wanted rather than learning to fall back to sleep on his own.
Hopefully this helps a little... Good luck to you - and believe me, it gets SOOOOO much better!!! I wouldn't be having another if it didn't!
Take care...
jess