Question 1. The minimum ring dimension that can satisfy a certain security level depends primarily on the multiplicative depth. It seems the multiplicative depth in your use case is large necessitating a ring dimension of 128K to achieve a 128-bit security level. Try to reduce the multiplicative depth which would allow for a smaller ring dimension while maintaining the desired security level. You can use bootstrapping to evaluate deep circuits if needed.
Question 2. This is not straightforward to answer. In a nutshell, the ring dimension does affect the precision as it affects the noise growth for certain CKKS operations (See Table 3 in this paper).