Hi,
I am afraid that the other stats (Average monthly searches, competition, etc.) based on your screenshot are not available to other services except the
TargetingIdeaService.
They are available as attribute types in the said service. For "Average monthly searches", it is equivalent to
SEARCH_VOLUME attributeType. For "Competition", the equivalent is
COMPETITION, and for "Suggested bid", the equivalent is
AVERAGE_CPC. Basically, the results based on your screenshot are supported in this service.
For your search terms also, you just need to use a valid parameter. For these three search terms in your screenshot, these are equivalent to
RelatedToQuerySearchParameter. With this parameter and attribute types, you can achieve an API result same as your UI result. You can also check this
example (available to other languages that we support) on how to do this.