Could these ICs from Alibaba be counterfeit?
For the question of the different numbers between the chips they are probably the date codes / lot number that many manufacturers use to track when and where a part was made. When customers report failures that can be useful to isolate manufacturing problems down to particular factories or batches. 

I couldn't find documentation for the DS1307 in particular but here's an example for another Maxim DS series part:

Clarification of DS1804 Ordering Information and Package Marking

For that part the final two lines are:

yywwrr
###xx


Where:


yy = Last 2 digits of year of assembly
ww = Work week of assembly
rr = Die revision code
### = Last 3 digits of lot number
xx = Up to 2 alpha characters of lot number suffix