Your questions are very interesting! They cut right to the heart of what many neuroscientists find fascinating about the brain and why we choose to study it. It seems you're perhaps asking a few different questions here: 1) do neurons need to be firing in order for a person to have thoughts?, 2) Which comes first--neural activity or thoughts?, and 3) Do thoughts come from individual neurons?
Do thoughts exist without firing neurons?
Essentially all neuroscientists believe that thoughts are purely an effect of firing neurons. That is, thoughts do not exist in the absence of firing neurons. When a person imagines hitting a tennis ball with a racket, for example, scientists see evidence of neural activity in the motor cortex--the part of the brain primarily responsible for movement--even though the person is lying completely still. When the same people are asked to imagine walking through every room of their house, starting at the front door, scientists see increased activity in the hippocampus, which is responsible for memory and for spatial navigation. We see more firing neurons in areas responsible for actually swinging tennis rackets and actual physical navigation in the world, despite the fact that the subjects are not receiving any external sensory cues related to tennis or to walking though their house. This finding implies that just the thoughts themselves require firing neurons.
In fact, these exact experiments were used to detect thoughts in people diagnosed with persistent vegetative state (see here and here). Persistent vegetative state means "complete unawareness of the self and the environment, accompanied by sleep wake cycles". Patients do not respond to sights, to sounds, to touch, or to language. Both doctors and family members, however, worry that their loved one can, in fact, see, hear, and understand them, but has no means of responding. This second condition, in which the patient retains normal cognitive function but is completely paralyzed, is known as "locked-in syndrome." Accurately distinguishing the two has obvious clinical and ethical importance. This test, in which doctors look for differences in brain activity as a person imagines swinging a racket or walking through their home, has changed the diagnoses of multiple "persistent vegetative state" patients and allowed locked-in patients to answer yes/no questions by imagining one scenario or the other.
Which comes first?
What these studies (and many others) suggest is that the process of thinking and the activity of neurons are deeply intertwined. One cannot have one without the other. We then come to your second question--which comes first? One way to address this question is to consider what happens when someone's neurons are forced to fire more, less, or differently from normal. Consider, for example, the use of deep brain stimulating devices to treat depression or obsessive compulsive disorder. Some patients try many different medications to treat their depression, but none of them work. In these cases, the patient may choose to have wires implanted, allowing doctors to send small electric currents through a particular brain region. This electric current disrupts the over-active neurons in that brain region, changing people's depressive or obsessive thoughts. In a recent clinical trial, doctors used this deep brain stimulation technique for otherwise-untreatable depression and bipolar disorder. Eleven out of 12 patients responded to treatment. Meaning, by changing how neurons in the brain fire, doctors can change how patients think and feel about the world.
Do individual neurons have thoughts?
The simplest human neural pathway I'm aware of has three neurons. This is the pathway that causes a person to pull their hand away from a hot surface. In this system, neuron #1 is a sensory neuron. This neuron has proteins on its surface that are activated by heat, and when the person touches, say, a hot iron, this neuron becomes active. Neuron #2 sits in the spinal cord. This neuron listens to neuron #1 and communicates its message "something is hot!" to neuron #3. Neuron #3 is a motor neuron. This neuron receives the signal from neuron #2, and fires to communicate with the upper arm muscles "Contract! Move away from the hot iron!". This neural circuit never even reaches the brain, so the corresponding behavior, contracting the arm, does not require the brain at all.
While all of this hand-to-spine-to-arm communication is happening, the signal of heat and pain is also traveling up the spinal cord, through a separate set of neurons, to the brain. Once there, the signal runs like an old-fashioned chain letter, contacting more and more neurons at every step. After less than a second, thousands or millions of neurons responsible for processing the touch sensations on the skin, generating the physical and emotional response to pain, and (hopefully) beginning the process of learning and memory will be active. And this, the "thinking" part of the process, the part that allows the person to perceive pain and to think " that was stupid! I'm never doing that again!" requires millions of neurons spread across the brain. There is no one neuron that tells the person "that hurt!" or "move away!".
To entertain the idea just a little bit, though, there are some examples of neurons that appear to be responsible for very specific ideas or thoughts. For example, the 2014 Nobel Prize in Physiology and Medicine went to three neuroscientists who discovered neurons that are only active at very specific places in the environment. If you could watch the activity of just one of these cells, you could tell, almost with certainty, where a person was standing in a room. In reality, these neurons are not thinking "you're standing by the ironing board". If this individual neuron were removed from the brain, the person would not be lost in that part of the room. Furthermore, if this neuron were removed from the brain and kept alive in a jar, detached from all its neighboring neurons, it would likely have no activity at all. These neurons are simply so far down the message chain, receiving the messages of many thousands of cells, that their output looks like thought. In reality, they are simply adding one additional computational step to the many that have already occurred.
Another fun example comes from researchers Itzhak Fried and Christoph Koch, who discovered what were famously referred to as "Halle Berry Neurons" and "Jennifer Aniston Neurons". These scientists showed subjects around 100 pictures of famous actors and famous locations, while monitoring the activity of individual neurons in and around the hippocampus. Amazingly, they found cells that respond to only one of those people or places. Furthermore, the "Halle Berry Neuron" responds to any picture of Halle Berry, whether she is in street clothes or dressed up as Catwoman. It also responds to the text "HALLE BERRY," suggesting that it is the concept of Halle Berry, not just her face or form, that drives this particular neuron's firing. It is likely, however, that this neuron would also respond to other people or places not included in the set of 100 images, and that other neurons in this brain region also respond to Halle Berry's likeness.
Individual neurons can have very specific responses--responses that might tempt us to believe the neuron is single-handedly responsible for the thought of a movie star, a famous location, or a distant relative, but this interpretation is (luckily) flawed. Although it simplifies the way we discuss brain function, and makes for good pop-sci fodder, a system like this with no redundancy, no back-up storage, would be exceedingly fragile. In the words of (at least) one great thinker: