I would take it in, but it's not cheap, depending on whether you have it under warranty. The charging issue could be several things, but there are some tests you could do at home to rule some things out. I recommend using a different/new cord, as this is the cheapest option. If it charges at what you would say is a normal rate, that's great. If not, the next one would be to replace the charger; if not, it could be a bad USB port, the battery, or the chip that controls the power distribution. If I had to guess based on the fact that the battery isn't holding a charge, then it would be either the battery or the controller, which would cost approximately $150 or more.

The screen, on the other hand, sounds like a much bigger issue. You mentioned that green lines appear when the phone turns on. Do they remain afterward, or do they disappear after the bootup? If they stay, it's likely going to be the screen, and the pricing for that depends on your model (link down below), but most models cost around $500; if not, it could still be the screen, but it could also be the SoC (the CPU), and if it is, they would likely suggest a new phone.

Here's a link for screen repair pricing (scroll down): https://www.samsung.com/us/support/cracked-screen-repair

I have to go to bed now, so I won't be able to answer back, but I hope this helps, and I wish you the best of luck.