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What is the way of emulating the Snap to Grid feature from the 3D Viewport in the UV Image Editor? In my case, vertices of my mesh are never aligned with gridlines, which in turn results in some artifacts on whole scene.

Also there is not consistency in mesh shape if perform "Lightmap Pack" as can be seen from image. Some of the actual mesh faces are more kite shaped, but map as squares or rectangles when it's "Lightmap Pack" unwrapped.

enter image description here

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You can use the texture image as a grid. In case you have no image loaded, create one. Then activate Snap to Pixel in the UV's menu. And when you move the UV vertices around in the UV Editor, then they will snap to the pixels of the image now.

For the other questions i would suggest to open other topics.

enter image description here

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I'm not a pro or anything, so maybe there's a better way than this, but I haven't come across it yet....

In my own experience, the UV mapper can only figure out so much. The rest is up to you. Instead of relying on the built-in mapping functions that are supposed to do it all for you, you will need to use a little selective face-choosing and placement within the UV editor. This can be tedious, but it seems to be the only way to do it and get acceptable results.

You can move the selected faces around in the UV editor, as well as scale and rotate, just as you do in the 3D viewer. That will help you to adjust textures on faces so they match up.

If you start with mapping the most squared faces but exclude the others, you can then minimize the work you need to do. With the remaining faces, you will now have enough room in the UV editor to organize them into the appropriate arrangement while aligning them to the other face's textures.

With the form that you're wrapping, there will be some mismatching where they converge together. That can't be helped.

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