The words don't have neat one-to-one match with English words. You can check these related words. - keep => 간직하다, 가지다; 계속하다(keep -ing); 유지하다. - save => 구하다(rescue); 절약하다, 저축하다. - maintain => 유지하다; 계속하다. - 가지다 => keep, take (in one's possession). - 간직하다 => keep, hold in possession with great care. - ~를 계속하다 / 계속(해서) ~하다 => keep/continue -ing. - 유지하다 => maintain, keep (in certain/good state). - 구하다 => save, rescue (other meanings: seek, come by). - 절약하다 => be thrifty with money. - 저축하다 => save money. - 이 사진 제가 가져도 돼요? => Can I keep this picture? (유지하다 won't work; 간직하다 is Ok). - 이건 중요한 물건이니까 잘 간직할게요 => This is an important item - I'll keep it with care. - 거스름돈[잔돈]은 가지세요 (잔돈 안 주셔도 돼요) => Keep the change. - 아이는 계속(해서) 울었다 => The baby kept on crying. - 소방관은 모녀를 위험에서 구했다 [구해 냈다] => The fireman saved the mother and daughter from danger. - 미래를 위해 저축해야 한다 => You should save money for the future. - 방은 18도를 유지하도록 되어 있다 => The room is set to maintain 18 degrees. - 유지와 보수 = maintenance and upkeep.

"Would it be okay to keep your picture?" => 당신의 사진을 간직해도 되겠어요? In common sense, in Korea, "keep + noun (ex. picture, memory, money...)" => "keep" is translated to "간직하다." ~ close to save. "keep + -ing (ex. working, saying,...)" => to "-을 유지하다". "maintain + noun (ex. building, system, ...) " also means "noun을 유지하다"

There are two verbs that you might want to look up on: 간직하다 & 지키다.