I wanted to convert 0-1v, 2ns pulse to 0-7v, 2ns pulse
To the inexperienced it sound like a "trivial" task to amplify the signal from 1 V to 7 V, right?

The problem is the speed you need for this. Your signal is 2 ns on, 6 ns off so that's 8 ns total, corresponding to 1 / 8ns = 125 MHz.

125 MHz is getting close to "RF" (radio frequency) signals, this means you have to consider parasitic capacitances and inductances of wires and traces on a PCB. Also even very small capacitances present in a transistor will ruin your day even at 125 MHz.

But it gets worse.

Since this is a pulse signal (not a sinewave) it is not just a 125 MHz signal, it will also contain harmonics of 125 MHz. Even for a half-decent looking pulse/square you need at least the 10th harmonic to be present as well. So 125 MHz then jumps to 1250 MHz = 1.25 GHz Oops! That won't even give you a decent rise time, as the rise time is still limited to 1  / 1250 MHz = 0.8 ns Oops again. How much risetime can you allow for ?

Sure amplifiers that amplify 7x with a 5 GHz bandwidth do exist but they require experience to use. You cannot just buy one if you don't know how to use it as the amplifier will only work when it has the right impedance at its input and output. Some impedance matching might need to be done. Yes, work for experts, not something anyone can do without the right experience. Many engineers who know what is required to make such a setup work call it "black magic". The magic wears off a bit when you understand it though.