The correct way of writing "morning" with nikud is בֹּקֶר, that is without vav. Some people also write it the same way without nikud - בקר, even though it is recommended to write it בוקר, with vav.
The reason why it is recommended to write it with vav is because בקר is usually understood as "beef" or "cattle", not "cow". It is pronounced "bakar". As far as cowboy is concerned, it is both written and pronounced the same as "morning", but a different syllable is stressed. "morning" => bóker and "cowboy" => bokér.
German and French both have the guttural (or uvular) r, which is what most modern Hebrew speakers use. Personally, I prefer to use a trilled r, similar to Russian or Spanish, where your tongue taps the roof of your mouth just behind your teeth. If you do that in modern Hebrew, people will understand you just fine, and it's a prettier sound IMHO. Whatever you do, don't use an American r with the lips.
In order for it to go through the translater I had to type it as morning or nite instead of morning or night. It took forever to figure it out. Why does Google Translater mess up on certain phrases? I have to type a " mark after some phrases too for it to type the correct word. ?????
Morning is basically the same as day. When someone asks "day or night", they mean the same thing as "morning or night," but "day" seems more natural. I guess "day or night" would translate to "יום או לילה", but when I first came across this phrase, I thought "day or night," even though I know בוקר means morning.
I see where you're coming from, but in my opinion, day and morning are the same in the way that "cat" and "animal" are the same. A cat is also an animal, but that doesn't mean you can translate "cat" as "animal", because the two are different concepts with separate, well-defined words in each language.