Driving during the afternoon, I noticed the sun looked beautiful. Driving during the afternoon, the sun looked beautiful. Yes, although notice the comma in the second sentence. Also it it sounds slightly odd because the first part doesn't give a time period but the second one seems to be talking about a specific afternoon. So unless there is a wider context to get this information it would be better to do something like this: This afternoon, while driving, I noticed the sun looked beautiful. This afternoon, while driving, the sun looked beautiful.

Sure, you could say that. It is clear that it is you who is noticing, seeing,.. it. Personally, I would have written ... Driving in the afternoon, I thought the Sun looked beautiful. 'during' would probably be very seldom said.

Oops, wrong compartment!

The first one is nearly accurate, but should be: While driving during the afternoon, I noticed the sun looked beautiful. Similarly, the second one may be corrected to: While driving during the afternoon, the sun looks beautiful. Notice that I changed "looked" into "looks" to match the tense of the verb "driving" in the beginning.

The "Driving during the afternoon" is describing the subject "I" here. So the subject has changed into sun in your version. In this case, the sun was driving during the afternoon which makes no sense because it doesn't have license to drive. :p You could say: Sinking into the horizon, the sun looked beautiful.