Here is the strawberry pest,

Identifying and control methods would be much appreciated!

Although it may be too late now, you could cover the mizuna with lightweight row cover if it's available where you live. Some folks even use very thin fabric such as tulle or netting.

The challenge for your current situation is that the beasts are already chewing,. So they area among your plants. So if you cover your plants, you're likely to also be tucking in the chompers.

Dan

i wanted to plant some more herbs and veggies in the same pot, can i do that w/o also infecting them with leaf miner?

could the chewer be slugs? don't slugs usually eat differently (bigger, more area covered), rather than just little dots?
Also, how do you suggest application of the neem? how to mix and should i just spray all over?

Interplanting species and herbs will help some. I do have a companion chart if requested to guide your mixed plantings.

Good luck. Dan