Your note on handseals manipulating chakra, that can be done regardless of handseals. Handseals are what allow the user to mold their chakra also allowing them to more easily concentration in doing so. Quite good on the rest of it. I have an explanation written out for both Chakra & Ninjutsu, if you have any questions are reading let me know^^.
Chakra:
You should also know that Chakra is comprised of both Spiritual & Physical energy of a living being, whether that being be human or animal, all creatures have a chakra network than runs through their system. Spiritual energy is thought of as being related to the being's mind & spirit, I would like to think that the more a living being is in tune with their mind & spirit, the more control they have over their own chakra, leading me to believe this is how one would gain a mastery over their "Chakra Control" a title used in many aspects of the Narutoverse. Physical energy is related to a being's body & vitality, something that can also be seen as one's inner strength & "Will". A life force with a greater physical energy would usually have a large source of chakra.
Chakra itself does not require to have an equal amount of both Physical & Spiritual energy. As noted some beings have a greater source of physical energy while others a spiritual. An example of a large source of physical energy would be the Uzumaki, a clan that is named for having large sources of chakra due to an extended life force. An example of spiritual energy would be the Uchiha, their Sharingan has a closer relation to spiritual energy rather than physical. This allows a Uchiha member to gain a visual prowess over such others like Senju or Uzumaki.
Ninjutsu:
Ninjutsu is a skill that allows one to control & manipulate their chakra, resulting in them creating a desired technique. There are two main portions of ninjutsu that are used to "enhance" a technique, these are known as Shape manipulation & Nature transformation. Shape manipulation gains the user the ability to alter the form of a given technique, allowing them to create a desire shape to an already existing chakra source of their own, this can allow the technique to gain a different effect than it's original form. Nature transformation is the basis of elemental chakra (the basic 5 elements being the most common used & in some ways the "pillars" to creating advanced nature types), something which consists of altering chakra's nature to gain a set of characteristics & properties.
Handseal are hand gestures commonly used to better manipulate/mold a user's chakra. it usually aids with techniques that would require more concentration, & gain an improved control over a technique.