What are the factors affecting expected difficulty and what is the maximum value it can take over the period of 30 days? Lets take for example day 1 difficulty of 300MM. What is the mechanism to determine the rise in difficulty?
What is the maximum value it can go starting from that number and expecting the biggest possible rise over 30 days?
The difficulty is not limited by a specific time-frame, but solely depends on the amount of hashing power available in the network. The difficulty is updated every 2016 blocks increasing or decreasing up to factor four. While the algorithm strives to set the difficulty such that it will always take about fourteen days for 2016 blocks, it could happen that the hashing power grows much faster than that: 

Scenario: Difficulty has been just set to 300MM, and somebody adds a crazy mining rig which is 20x as fast as the whole network


The network is now 21x faster than what the difficulty tries to balance
2016 Blocks are mined in 16h instead of 14d
Difficulty quadruples to 1200MM, the next difficulty reset is reached after another 64h (2d 16h)
Difficulty quadruples again to 4800MM,  the next difficulty reset is reached after 256h (10d 16h)
Difficulty finally catches up with the hashing power added and only increases by 21/16.


In this scenario it would take the network (16+64+256)/24=fourteen days to increase by factor 21. Imagine that our great engineer figures out how to first build one of those super-rigs a day and then speeds up the progress. Theoretically the difficulty could increase by factor four every hour all 30 days (which would be a factor of 2880).

In other words, there is no maximum value for the difficulty in the next 30 days.