Your photo is a little unclear. But firstly, it's not a fern. Looks like Chamaedorea elegans, Parlour Palm. And yours will be a multiple planting, something nurseries do to get that full look in a pot. They plant a handful of seeds so you get many plants. Some of the weaker seedlings get smothered and die out, the stronger ones dominate. Since you're loosing a lot of still green plants then it suggests they're too dry. You can check with a wooden skewer, pushing it down into the soil there'll be damp soil sticking to it or signs of moisture when you pull it out, otherwise it needs water. Indoors air can be very dry so fast draining soils dry out even faster. They can cope with low light but bright light is good. Don't allow direct sunlight. Keep damp but not soggy. They're quite a tough plant for indoors.

Yes, Mr Blubs is right that your plant has scale insects. How important is this plant to you? If this plant isn't sentimental or valuable, it may not be worth it to try to fight the scale. Scale can be tough to eradicate. If you really want to try to save the plant though, I would suggest using a systemic pesticide that is labeled for indoor use in addition to following the advice to spray it (as well as the pot and the surrounding area) with a mixture to try to kill the insects every few days for several weeks.

Thank u for the help! I thought so too but have no idea how to make a hole in that pot as it's made of cement. The only way is to drill :) Is it possible to do it now when the plan has been in the pot for some weeks? Or am I going to disturb it too much so it will die? I also thought about removing some soil and replace it with new dry soil of the same type. There are some new big leaves opening now. Alex

100% Normal. I use the trunk/petiole fiber on mine growing outdoors to line baskets and like that.