Intrinsic motivation typically arises from internal desires, such as personal enjoyment, interest, or a sense of satisfaction derived from an activity itself.
Yes, but typically only in the short term. For example, external factors such as praise and public recognition, material rewards; persuasion, suggestion, hypnosis, and other manipulations can enhance internal motivation. However, long-term internal motivation is usually stable and resilient to external influences: it can only be changed by the individual making volitional efforts. An example would be personal development through interventions by a psychotherapist. The psychotherapist engages in conscious intervention in the client's consciousness with the aim of changing their neurotic patterns, yet it is ultimately up to the individual to determine their motivational changes
"Can intrinsic motivation be inspired by external factors?" --. You ask.
I may be wrong, but my answer as a psychologist is a definite "NO". By definition, intrinsic motivation is due to intrinsic, not extrinsic motives. As the USA psychologists Edward L. Deci and Richard M. Ryan put it, intrinsic motivated behaviors are self-determined.
See, for this respect, their work on their Self- Determination Theory. In few words" Self-determination Theory (SDT) is a motivational theory of personality, development, and social processes that examines how social contexts and individual differences facilitate different types of motivation, especially autonomous motivation and controlled motivation, and in turn predict learning, performance, experience, and psychological health. SDT proposes that all human beings have three basic psychological needs – the needs for competence, autonomy, and relatedness – the satisfaction of which are essential nutrients for effective functioning and wellness. Satisfaction of these basic needs promotes the optimal motivational traits and states of autonomous motivation and intrinsic aspirations, which facilitate psychological health and effective engagement with the world." (Retrieved from the Internet).