Title only makes sense when you read it with the prefix xD
Using a car as a metaphor for one's body, chakra is the fuel, handseals are the steering wheel and ninjutsu is a distance travelled. Chakra is a lot of things, but in this context I'll say it's the spiritual energy responsible for performing actions. Just as energy drives the world, energy drives our entire system (which would be the entire career in this analogy). Similar to how a car burns fuel to travel distances so do we also utilize or "burn" chakra to perform ninjutsu. Thus, in the most basic terms, ninjutsu is the product of chakra utility. Just like how a car cam travel in any direction when directed, so can we perform various actions depending on the direction we steer towards. Therein lies the function of handseals and what they inherently are. Handseals stipulate, for lack of a better word, the work that is to be done by chakra. A steering wheel determines if a car should go left or right; handseals, in collaboration with molding and manipulation, determine what ninjutsu product should be formed from the chakra being expended.
The primary difference between ninjutsu and genjutsu is that while the constructs of ninjutsu are real, those of genjutsu are purely imaginary.
Nicely defined, but your definitions are vague. I liked it though. And, you're correct. Effects of Genjutsu are imaginary, except for Kurama clan. They can make the effects of Genjutsu real.
Chakra: "Chakra" is basically life essence or life force which exists in human bodies and animals. Without it, a shinobi can die. It can be considered "blood" and soul for a ninja. It is the molding of physical energies and spiritual energies in the body. Physical energy is the energy given off by the body cells and can be increased with more stamina and practise. Spiritual energy is derived from the consciousness of the mind and can be increased through great concentration and meditation. It is the basis for all almost all the ninja skills like Ninjutsu, Genjutsu, except Taijutsu in some special cases. It flows through the chakra circulatory system, and in it, there are 361 points aka nodes in the body known as tenkutsu. The function of the tenketsu is to regulate and control the flow of chakra. If these weren't present, then chakra would flow through some specific organ, thus there wouldn't be a balance in the chakra flow. Every ninja in the narutoverse possesses a chakra pool. Shinobis with a very high chakra pool like Naruto can perform a lot of higher ranked techniques like Multiple Shadow Clone Technique, etc. without having the fear of getting their chakra depleted at once. Senju Clan members for eg, have very high chakra reserves and a high physical energy aka high "Yang" energy, thus their naturally strong bodies and on the other hand, the Uchiha clan members have a very high spiritual energy, i.e. high "Yin" energy, thus their proficiency in genjutsu and visual prowess. It is possible to have high chakra if you possess very strong willpower. If chakra runs out completely in a shinobi, then he dies as shown when Kakashi died due to his chakra completely running out against Deva Pein. It can be divided into several types like:
Elemental Chakra
Senjutsu chakra
Bijuu Chakra
Ninjutsu: Ninjutsu means "Ninja Arts" and is something that allows the shinobi to do something that a normal human can't do, like walking on water, manipulating elements, the usage of special as well as bladed weapons, stealth, transformation, etc. The effects of ninjutsu are real. Most of the time, it heavily relies on the usage of handseals as well as chakra. Regular ninjutsu doesn't incorporate the usage of elements for it, like stealth, a basic Rasengan, etc. Elemental Ninjutsu is an advanced form of ninjutsu, which incorporates the usage of basic 5 elements, as well as advanced combinations to create stronger jutsus which have the respective properties of the 5 elements. Elemental ninjutsu is stronger to regular ninjutsu, since regular ninjutsu only uses raw chakra, whereas, elemental ninjutsu uses both Shape Manipulation and Nature Transformation. The perfect Rp example would be that, a Wind natured or a Lightning natured Rasengan would have a greater destructive force than a standard Rasengan, obviously because the elemental Rasengan contains violently rotating chakra as well as the violently rotating chakra is given the property of the respective elements.
Handseals: Handseals are hand gestures, which primarily manipulate chakra and dictate the exact amount of chakra needed for the respective specific technique. Weaving of handseals makes chakra take different "patterns". Some techniques require a large number of handseals, which is related to the complexity of performing that technique and if not weaved properly, in order, or if the user loses focus in between, then the technique is either executed in a weaker state, or it is dispersed midway, depending on the specific technique. A good example is Water Dragon Bullet Technique. It was shown that the technique required a string of 44 handseals to perform, however the Second Hokage, Tobirama could perform it with a single handseal, due to his unparalled Water mastery. It is shown in the manga that with time, a shinobi after mastering the specific technique, requires one-literally no handseals to perform it, an example being Chidori, which required some handseals when Sasuke just learnt it. In our RP, the user can perform any 2 elemental releases of his choice, depending on the elements he has placed as specialties, with one-virtually no handseals/faster handseals. Usually, handseals are performed with both the hands, but Haku, Minato, etc have demonstrated the ability to perform it with only a single hand. The 12 basic handseals are Monkey, Ram, Dog, Horse, Dragon, Boar, Rat, Snake, Ox, Hare, Bird, Tiger.
Genjutsu: Genjutsu are the illusion arts of the narutoverse and in our RP. If Ninjutsu is produced through the harmonization of Yin and Yang chakras, Genjutsu is primarily the Yin portion as it focuses on the aspects of creation and the imagination as opposed to reality. Genjutsu is the process of manipulating the basic five senses and, overall, affecting the mental state of one all together to produce illusions and mentally attacking entities. Unlike nin and taijutsu, the effects of genjutsu are not real bar few exceptions. The basic mechanics of genjutsu are; the disruption of one's opponent's chakra system through syncing and infusing their own chakra through to their brain and controlling the cerebral nervous system. The result from the chakra disruption causes an irregular flow of chakra that will result in the brain to process and project the contents of the illusion of the user. This is how most conventional genjutsu techniques work and force one to experiences an illusion. The entities of an illusion are presented as real to the senses which result in mental damage while the physical body is completely safe in most occasions. There are various types of genjutsu and various methods of genjutsu users who emphasize different types of illusions. Genjutsu, as a spiritual entity is often times over looked and/or underrated by many as it typically cannot get the job done to completely incapacitate or kill your opponent which is the desired. Genjutsu is typically used as a distraction tool or a tool of hindrance to set up for a more advantageous ninjutsu. In the series it is typically stated that only smart/intelligent shinobi are even capable of using genjutsu because of how advanced and difficult it is. Though in the case of the RP any and everybody can use genjutsu but typically only those who have a real knack for the style and skill for it are capable of using it well. However there is always a huge issue with metagame and inadequate use with genjutsu most times.
Now, unlike other abilities, for Genjutsu, there are pre-methods to go through, before we start the method system. Any doubts?