Electrical – How much voltage difference will lead to saturation, LM741

This is really simple - use an N channel FET and have it as a source follower. You can even use a BJT. The one below has gain due to the 3k3 feedback and the 1k to ground from -Vin. If you don't want gain connect the output directly to -Vin and omit the 1k.

A unity gain buffer on the output of an op-amp is either an emitter follower or a source follower. Simple as that - feedback from the emitter/source back to inverting input of the op-amp.

Additionally, because the source/emitter voltage "follows" the op-amps output signal, the gate/base loading effects are minimal hence when using a MOSFET you don't need to worry about gate capacitance.

Think about this sensibly - Analog Devices or TI or MAXIM of LT - their marketing team are not going to wake up one morning and say to their designers - why can't you design an op-amp that allows someone to add a gain stage on it and expect it to be stable. If they did, the designers would say that they'd have to reduce the performance of the op-amp for it to be stable - just how would that op-amp compete in the market against all the op-amps that take the sensible road and keep building what they are good at.

Several op-amp parameters combine to indicate what the "delay time" there may be for a given circuit configuration but, in critical timing situations I would strongly consider routing the "direct" signal referred to, thru a similar amplifier configuration so that these delays largely cancel.

The single parameter I would most focus upon as an indicator would be frequency at which the gain becomes zero (also called GBWP, gain-bandwidth-product) but slew rate (the op-amps ability to change its output voltage in volts per microsecond) can also have a part and so can settling time.

Op-amps with greater GBWP will have a smaller delay at any given frequency.

The closed-loop gain is also important - the higher the closed loop gain is the more the output phase tends to lag the input by 90 degrees. 90 degrees is the natural phase angle for most open-loop op-amps due to stability circuitry within the op-amp. When the loop is closed (by feedback) the phase angle becomes dominated by the feedback components but this gets gradually eroded towards 90 degrees as frequency rises. This happens because open-loop gain falls at higher frequencies and the effect of external feedback reduces and the internal 90 degree phase shift starts to dominate.