First Try resetting the SMC, If this doesn't work then I would suggest replacing the battery. Just make sure not to buy a cheap battery off of eBay; I would recommend the cheapest battery being $40. I replaced my old battery with this one from Amazon.
Have you tried resetting the SMC, and/or PRAM? Most of the time you can fix a MacBook with these commands. If these don't work it might be a display issue, try checking if the display cable plugged into the logic board is loose. Try taking it out and plugging it back in again. You could also see if it is just a bad display by hooking it up to another monitor. If nothing displays to this, then it is a graphics chip issue. If the monitor works then you will need to replace the display assembly, if nothing displays then you can try checking the drivers. This most likely isn't the issue and it is probably something with either the logic board or the display.
Try replacing the thermal paste. Apple's thermal paste is not very good at effectively cooling their computers, even the newer models. I had a similar issue with my mid-2009 MacBook Pro, where just opening a website would shoot the temperature up to 180°! I replaced it with some thermal take thermal paste and the temperatures would max out at 140°. You could also try installing Macs Fan control which allows you to control when your fan will start to spin faster or just to spin fast all the time. I would recommend setting your custom setting to CPU proximity and the min to 100° and the max being 132°.
Try checking your playback devices by right-clicking the sound icon in your taskbar, and selecting your headphones. If this doesn't work, check if you have the proper drivers installed, or try uninstalling the current driver and reinstalling it.
Use laze soft password recovery, this tool won't give you your old password, however, it will completely remove the password, allowing you to create another one. All you need is a USB flash drive with the software installed, then boot up off of the USB from the boot menu on your computer. Download
Assuming that you are using final cut pro or iMovie, Apple does a really good job of optimizing their software for each of their computers. I would suggest the mid-spec 21.5 inch 2018 iMac with the storage option set to fusion drive. I would recommend this because it has a quad-core i5 and 2gb gddr5 graphics memory so you will be able to edit videos pretty well without leaving you bankrupt. I would suggest you upgrade to a fusion drive because the standard hard drive is very slow for a new computer. The Fusion drive combines a hard drive and an ssd so you will have quick boot times but a lot of storage for your video projects. As for memory, you can leave it stock with 8gb, but 16gb will last you longer and is really a better deal. If you are looking to upgrade your current iMac, then unfortunately you can't upgrade the graphics performance, ram, and CPU since those are part of the logic board. iMac
It could be the pins on your charger if it it the original. I have the same issue with my older MacBook Pro(2009). You could try replacing the DC in board, or using a newer charger if it really bothers you.