Hi there. I think the most important thing right now is to establish a more appropriate routine and work on independent sleep--getting her to fall asleep in her crib without you. Many babies are her age do need at least one night feed, so it's not surprising if she does, but once you have A times figured out and she's sleeping independently you'll be better able to figure out the cause of her wakings.
The bedtime struggles really do sound like overtiredness. To help deal with overtiredness you can try
A) reducing A times in 15 minute chunks, so for now, move back to 1 hr 45 minutes
b) moving bedtime up--try no later than 7 p.m. if she's waking at 5:30 - 6. Temporarily you might try even earlier, 6 or 6:30 to help deal with the overtiredness.
As for getting to 3 hour EASY--you can try extending naps to make it to 3 hours using w2s, pat/shush, pu/pd, or a combo. We had success by going in when dd first stirred and gently patting, and the key was getting in there before she woke fully. If she wakes at 45 minutes, spend the next 30-45 minutes trying to get her to go back down up until the next feed time. When she gets back to sleep you then wake for the next feed, but at this age she can probably stretch feed times to 3.5 hours or even a bit longer, so you don't need to wake to feed right at 3 hours.
You'll need to use a sleep training technique to work on independent sleep at all naps and at bedtime. Yes, you should use the same technique for day and for night. At your los age you should start with pat/shush and only progress to pu/pd if needed. Your lo is on the young side for pu/pd although it does work for some at 4 months--make every effort to calm in the crib but pick up if needed, put down when calm, etc. With very spirited los it's sometimes best to avoid too many pickups as this can overstimulate.
Pat/shush link:
https://babywhispererforums.com/index.php?topic=26672.0Pu/pd link:
https://babywhispererforums.com/index.php?topic=69177.0 w2s for extending naps:
https://babywhispererforums.com/index.php?topic=64107.0Good luck and let me know if you have more questions! HTH!