There is a soft g (which is pronounced as the Y in "yet") and a hard g (which is pronounced like the G in "goal"). Which one of these you should use depends on what vowel follows, similar to English. It is, however, never pronounced like a french J, although the soft G may be slightly fricative in some dialects, same as the letter J.
In this case, the G in "god" is hard while the G in "morgon" is silent.
I was referring to the "D" in this sentence. I don't think there is a general rule when to drop the last consonant, but in a lot of short words ("det", "god", "jag", "mår", etc.) the last consonant is often dropped, unless there is an emphasis.
As for general pronounciation of Swedish, pronounciation is not that important when learning Swedish. You learn pronounciation by listening to native people speaking, but a simple google search can lead you to a lot of good material if you are curious.
Most dialects have a trilled R, which is often reduced to a flap or an approximant in speech, in some dialects the R is more noticably trilled. In Scania, Blekinge and parts of Småland the R is guttural and is pronounced like the French R. In some dialects in Västra Götaland the R is guttural if it's the first letter of the word, but trilled if it's elsewhere.
So it is a bit complicated. My personal recommendation is to trill the R slighly, this is the most "neutral" way to pronounce it.