You could say
The course will start on December 2nd and run for 4 weeks with 4 hour sessions every Monday and Wednesday.
or even
The 4 week course will start on 2nd December. 4 hour sessions will be every Monday and Wednesday.
Maybe breaking the original into two simpler sentences will make it clearer.
Since writing the above, you have added version 3
This 4-week course will start on December 2 and each session runs for 4 hours every Mondays and Wednesdays.
Which contains a minor error. You can either say
...each session runs for 4 hours every Monday and Wednesday.
or
each session runs for 4 hours on Mondays and Wednesdays.
Regarding your additional questions, minor corrections again
1 The course will start on December 2 and will run for 4 weeks with 4-hour sessions every Monday and Wednesday
or
1 The course will start on December 2 and *will run for 4 weeks with a 4-hour session every Monday and Wednesday
and similarly
2 The course will start on December 2 and runs for 4 weeks with 4-hour sessions every Monday and Wednesday
or
2 The course will start on December 2 and runs for 4 weeks with a 4-hour session every Monday and Wednesday
However, as Mary and I have already pointed out, it would be better to simplify your sentence, possibly in the way I originally proposed - break it into 2 shorter ones with one idea in each.