'schwer' can mean 'difficult' but in this particular sentence it normally wouldn't be understood that way. If you want to express that the elephant is 'difficult' (in whatever sense that may be) you can use 'Dieser Elefant ist schwierig'.

Sounds fine to me. Note that the quality of the 'e' at the end also changes depending on whether it is 'diese' or 'dieser'

The unaccented -er ending often sounds like -a.