Cycling distance per day
When I decided to get back in biking around 2 years ago (After not being in a bike since I was a teen) this was around the same amount of distance I had to pedal. My bike was a Schwinn Ridge Al mountain frame with slick tires and during the first week I couldn't complete the commute for more than 2 days in a row. After the second week it became a lot easier and since then I commute by bike almost everywhere within 20Km. 7Km is quite a small distance but depending on your current fitness you may need to bike only 3 out of 7 days the first week (With resting in between). After that it will became really easy for you. 

I checked your route using the Google Streetview and found there are a lot of bicycle taxis out there, which suggests these roads are plenty used by bikes and you should have no problem with traffic speed, but be very careful with the basic cycling safety measures. Sticking to the same traffic patterns should help to make things safe enough, but you may want to ask fellow cyclists for tips. 

If you already own a bike, give it a try on any free day! That will let you have a better understanding of what will be required.