Q1: I am using the DS1337 RTC in an embedded application. After reading through the data sheet it is not clear to me how to specify the fast or standard mode regarding the I2C bus speed.
The DS1337 operates as a slave on the I2 C bus. Within the bus specifications a standard mode (100kHz maximum clock rate) and a fast mode (400kHz maximum clock rate) are defined. The DS1337 works in both modes. You don't need to set any thing on DS1337 it depend son the clock frequency of the I2C Master. As long as the clock frequency is less less than or equal to 100kHz the device will operate in standard mode. For Master clock frequency between 100k and 400k the device will operate in Fast mode.
For more information please see the I2C specification
https://www.i2c-bus.org/specification/
Q2: My concern with continuing to run my I2C bus at near the 100k Hz threshold was that the DS1337 could possibly switch over to fast mode if it somehow detected a frequency above 100k Hz.
Ans: There is not a instant change at 100k Hz from Standard to fast mode. As long as you are running at 100k Hz you can safely run in standard mode. Fast mode activates when the frequency is near 400k Hz
Q3: The DS1337 spec states that the max rise time for either the data or clock lines is 1000nS. The rise time for my data line is 810nS and 718nS for the clock. This is getting fairly close to the 1000nS spec. I am using 10K pull up resistors for both the SDA and SCL lines.
Ans: A stronger pull-up with 4.7k resistor will reduce the time constant of the rise time. You should experiment this and measure the reduction in rise time you can achieve.
