Gassy Baby- 4 month old

My daughter is 4 months old.
She is very gassy. It doesnt seem like she has any pain but keeps passing gas frequently. It is smelly. There’s mucus in her stool almost everytime she has a bowel movement. She has a bowel movement once a day and sometimes skips days. But its always soft.
First 6 weeks she used to wake up often (every 2 hrs at night). Then at 2.5 months it got really better at night- sleeping at a stretch of 8 hours straight and then waking up a couple of times after. Day time naps were minimal though. Used to sleep only 1-2 hrs total and that too for only 30 mins at a time.
At around 3 months this changed to 6 hour stetch at night. And then at 3.5 months, she started waking more frequently like every 2-3 or 3-4 hours.
She likes to sleep more during the day now. But, only sleeps well while breastfeeding.
She is 100% breastfed and has not been vaccinated.
She was very impatient kind of baby until 6-8 weeks. Now she is a very happy baby.
She smiles a lot and also makes a lot of sounds. She is very interative. We never have to carry her around. She can lie down or sit in rocker for a long time.
She loves massage and bath time.
Her feet get cold pretty quickly.
She is tall (80 percentile) and has a big head(80% percentile). Weight is in 50 percentile.
She has been drooling a lot since she was 2 months. She makes kind of bubbles like drool.
She has a very dry skin. Her legs become very dry-it looks like skin peeling and scaly. We apply a lot of coconut oil and that makes it better.
She has a liptie but we are not sure if we should get it clipped.
[Edited by Soothe on 2017-10-16 15:33:23]