1 mm thick steel is pretty thin to be using .6 mm wire on... I would suggest something more along the lines of .023 or .025mm. I have never used anything thicker than .035 and that was on 1/4 inch plate with a 440v 100% duty cycle welder. So the biggest part of your trouble is that you are using too thick of a welding wire... spend a few bucks and get the proper diameter wire... it will save you tons of headache and your welder will perform better!
I would also suggest that you do a continuous bead with the lap and butt as has already been suggested... with this change... I noticed in your first pics that your welds were quite squiggly... NEVER WELD MIG FREEHAND! If you are right handed, hold the gooseneck with your right hand, make a fist with your left hand and set it on something solid close to where you are welding... like the firebrick you are welding on... then drape the gooseneck over your left hand fist so that you won't be moving around when you are welding.
There is simply too much wire exiting the contact tip to weld mig freehand... you can weld stick, oxy, and tig freehand b/c they deposit so much less filler... mig is different... your hands have to be steady and the only way to do that is to rest them on something solid.
If you are having trouble seeing your bead I would suggest turning down the shade on your auto tint helmet and moving your head to the side so that you can see better.
With thin metal... like 1mm always forehand weld... think of a forehand slap... vs a backhand slap... I'm right handed and so I forehand weld from right to left... this is for the lap weld and you should have no gap and a very tight fit up... very important!
For the butt weld, you should have a gap at least as wide as the metal you are welding on and I completely agree with the weave... the only difference I'm going to suggest here is that you change the position of the metal so that the gap points away from you... like your arm (or other appendage) would point away from you if you were to point at something in front of you... then start welding furthest away from you and move closer using that very slight but quick weaving motion... your gooseneck should also be angled away from you.
I would also suggest that you do a continuous bead with the lap and butt as has already been suggested... with this change... I noticed in your first pics that your welds were quite squiggly... NEVER WELD MIG FREEHAND! If you are right handed, hold the gooseneck with your right hand, make a fist with your left hand and set it on something solid close to where you are welding... like the firebrick you are welding on... then drape the gooseneck over your left hand fist so that you won't be moving around when you are welding.
There is simply too much wire exiting the contact tip to weld mig freehand... you can weld stick, oxy, and tig freehand b/c they deposit so much less filler... mig is different... your hands have to be steady and the only way to do that is to rest them on something solid.
If you are having trouble seeing your bead I would suggest turning down the shade on your auto tint helmet and moving your head to the side so that you can see better.
With thin metal... like 1mm always forehand weld... think of a forehand slap... vs a backhand slap... I'm right handed and so I forehand weld from right to left... this is for the lap weld and you should have no gap and a very tight fit up... very important!
For the butt weld, you should have a gap at least as wide as the metal you are welding on and I completely agree with the weave... the only difference I'm going to suggest here is that you change the position of the metal so that the gap points away from you... like your arm (or other appendage) would point away from you if you were to point at something in front of you... then start welding furthest away from you and move closer using that very slight but quick weaving motion... your gooseneck should also be angled away from you.