There are many sources of circuits for old CRT TVs. Why not obtain some even if they are not for your specific unit, and study them?
Also, if you live in any kind of western urban setting, free CRT TVs are easily found. People are throwing out all kinds even large, relatively 'modern' perfectly working ones, as they buy nice LCD TVs. So you could probably find more to play with if you wanted.
As for the beam intensity control - they don't use the grid to control beam current. The grids are typically set at fixed voltages that interact with the focusing rings to give correct beam geometry. And they're not really 'grids' - they're discs with a little hole in the middle. Get some old CRTs, crack the little pump-out nipple under the rear plug molding to de-vacuum the tube safely, then smash the neck open to examine the electron gun. They're pretty!
Beware - the screen phosphors, coating on the cathode, and the substance in the 'getter' ring are all really poisonous. Don't inhale the dust, don't get in cuts, wash hands after, etc.
Beam current is controlled by varying the voltage on the cathode. The more negative, the stronger the beam.
If you look at the small PCB typically mounted on the tube rear socket, it will have either one HV transistor (monochrome tubes) or three (RGB.) These drive the cathode(s). I vaguely recall the transistors are typically driven in common-base arrangement, since that gives the best voltage-gain/bandwidth.
If your CRT is from a TV, you'll find it very hard to drive the deflection yoke with high enough frequency of current variation to generate much text on the screen. TV yokes are optimized for operation at the H and V scan frequencies, and in the case of the H deflection coil, typically their inductance forms a part of the overall flyback oscillator system. But maybe, on that small a tube the yoke will be fairly small and low inductance too.
Hmm... Somewhere I have the schematics (and a working display) from an old Atari Asteroids arcade game. That basically does what you're trying to do, but with a larger B&W TV screen with deflection yoke. Want me to find it and scan it? The deflection drive circuits are non-trivial, I warn you. And I think they used a custom yoke.
Oh and one more thing. A TV CRT electron beam is quite capable of drilling a hole in the back of the screen glass, if you leave it in one spot while bright. I killed a screen that way once. The Atari system had a spot-killer circuit, that turned the beam off if there was no deflection happening. This is _why_ CRT TVs used the yoke as part of the EHT oscillator circuit. No yoke, no EHT, no screen burn.