I put these examples particulary because there is misunderstanding with color count in print design. White is not always an empty color, it's just a default background of canvas in software.

I would better say don't ever rasterize type and vector objects. If possible, put type on top of any other parts. If not possible, for final solution, remember to rasterize all transparency effects (also layer semi-parentness or some kind of overlay). Do not send tiff file. It's totally superold format, useless size. Better flatten and send psd.

What version of Illustrator are you using?

It just can't be black because you are not painting it black. You paint it 50% transparent. You can use another trick, if the transparency for all painting job is the same: paint it with 100% black and change the opacity of the layer.

I added to answer method of getting black value on the new layer.

You can flatten copy of image. Image -> Duplicate.

It's actually pretty simple so I don't know what to explain more. You have a layer with color + transparency. If you flatten image, you will remove transparency, but will get precise color. In you example if it was 50% gray rgba(255,255,255,0.5) then with flattening it will become simply rgb(128,128,128) without transparency option.

If you have your own ideas, then present them to the client. If you don't have any ideas, then you have two choices: 1. Make logo the client wants. 2. Loose a client.

I heard only one important reason - compability with Lightroom. And it's not essential for a lot of users. And in case with raw photos from camera I still prefer to use dng, not psd file format. Just because dng is made axactly for this reason and psd is not.