I recently bought an Anet A8 (https://pevly.com/anet-a8-3d-printer-review/). I've managed to get everything up and running, leveled the board, but am now running into a problem.

At the start of the print, the printer moves to 0,0,0, bumps into the switches a couple times (I assume to calibrate or so?), and then starts "printing". But the nozzle "randomly" moves to either an X of 0 or an Y of 0 before returning to the printing position. This movement seems to pull off any basis the printer managed to lay down, which then forms a nice "ball" on the nozzle, to which the rest gets stuck. (I'm still having some other issues with getting the filament to stick to the bed, but there's plenty I still have to try out for that.)

During one attempt of printing a very simple small cube, I carefully pulled the filament "ball" from the nozzle while it did one of those movements to X 0, and afterwards it managed to lay down the bottom layer perfectly fine. This causes me to believe those movements are the biggest problem I'm facing right now.

After it did the first layer, it moved up a bit, moved to X 0, back to the model, and got stuck on a piece of plastic that was standing upwards.

These movements seem to happen at around the same phase in the print, and happen quite consistently. Is this normal behavior? If so, how do I make sure the filament does not get pulled off during these weird movements? If not, how do I get rid of them?

(No, not a duplicate of Printer randomly moves to home during printing, then resumes as normal as I print directly from PC.)

Edit to add more information:

I use Cura 3.0.4 for printing, the stock Anet A8 firmware, and am attempting to print the cube model that comes with Windows 10. (Yes, I've tried different models, same result.)

I seem to have more issues, in the video it's visible that the feeding does not seem to work too great, but I think the random movements are the most clear and biggest problem right now, so I should tackle that first.

In Cura I've used the Pruisa I3 printer, with the following G-codes:

G21 ;metric values
G90 ;absolute positioning
M82 ;set extruder to absolute mode
M107 ;start with the fan off
G28 X0 Y0 ;move X/Y to min endstops
G28 Z0 ;move Z to min endstops
G29
G1 Z15.0 F9000 ;move the platform down 15mm
G92 E0 ;zero the extruded length
G1 F200 E3 ;extrude 3mm of feed stock
G92 E0 ;zero the extruded length again
G1 F9000
M117 Printing...

and end

M104 S0 ;extruder heater off
M140 S0 ;heated bed heater off (if you have it)
G91 ;relative positioning
G1 E-1 F300  ;retract the filament a bit before lifting the nozzle, to release some of the pressure
G1 Z+0.5 E-5 X-20 Y-20 F9000 ;move Z up a bit and retract filament even more
G28 X0 Y0 ;move X/Y to min endstops, so the head is out of the way
M84 ;steppers off
G90 ;absolute positioning

(Yes, I added in the G29 in the start code manually, as I bought the official auto-leveling sensor. I'm not sure if it works though, but I read somewhere that I might need a different version of the firmware to support it properly.)

And here's a video showing what my printer does do exactly. It started printing from the center in this case, it seems to randomly either move to the middle or to 0,0,0 when I abort the print.