1) Yes, it makes sense (more or less) in terms of conveying meaning. However, a more elegant way to phrase it might be:
Today, people have more information available in regards to health issues.
The main problem with your statement, as I see it, is:
"Modern people" sounds very vague.
"Raised awareness of health" literally means to have brought up, to have conceived of, the topic of health. Of course, that is not true. Today, we are simply more aware due to advances in medical technology, the ability to spread information etc.
2) Modern people attach more importance to their health
Yes, this is correct. But is it true? I know you ask simply for the English, but I would think carefully about making such a claim!