How can I check in an OpAmp datasheet if the OpAmp is push-pull?
As you seem to be focusing on the Rail to rail aspects, it is necessary to read the datasheet of any potential device.

Using your LMH6645 as an example, we can evaluate if the device is suitable. If I assume you have a 10 bit DAC running on 3.3V, then each lsb is about 3.2 mV.

It would be wise to choose an amplifier where the \$V_{OS}\$ term is well below that to avoid DC offsets.

For this device, \$V_{OS}\$ is typically +/- 1mV (max at 25C is +/- 3mV) so this would not necessarily be my choice of buffer for a DC or low frequency application, but a great deal depends on context.

Leaving that aside, let's see what type of rail to rail input is employed. There are a couple of types with the most common being a dual overlapping input stage.

To find out if that is true, we need to look at the \$I_b\ vs\ V_{cm}\$ graph (not every device has this).



Note that the direction of \$I_b\$ reverses as the common mode voltage is varied; this means that the input is an overlapping input stage (a PNP stage and an NPN stage).

Some text in the datasheet shows that the crossover is not actively steered which means the actual crossover point will vary from device to device and over temperature:


  The total input common mode voltage range, which extends from below V−
  to beyond V+, is covered by both an NPN and a PNP stage. The NPN stage
  is switched on whenever the input is less than 1.2 V from V+ and the
  PNP stage covers the rest of the range. In terms of the input voltage,
  there is an overlapping region where both stages are processing the
  input signal. This region is about 0.5 V from beginning to the end. As
  far as the device application is concerned, this transition is a
  transparent operation. However, keep in mind that the input bias
  current value and direction will depend on which input stage is
  operating (see Figure 29). For low distortion applications, it is best
  to keep the input common mode voltage from crossing this transition
  point. Low gain settling applications, which generally encounter
  larger peak-to-peak input voltages, could be configured as inverting
  stages to eliminate common mode voltage fluctuations.


So if you want a really low distortion buffer then you would need to run this device from a power rail at least 1.2V higher than the signal you are buffering (so that the input signal does not enter the transition region) Over temperature, you would really need to run this from a supply at least 1.5V higher than the DAC output.

If you can do that, then this device might still be suitable.

Note: This type of input stage is prone to low level oscillation in DC applications with a high source resistance; whether it would be noticeable depends on input bias current.

Now for the output:

The output can swing to within a low voltage with respect to the power rails (it cannot be zero as there is always some output resistance).



This particular part of a table is from the 5V section of the datasheet and we can estimate the effective output resistance of the device:

Using the worst case, into 1k at 2.5V (1/2 V+) the output can swing to within 200mV of the power rails with 2.5mA load; that means the output resistance at these points is (worst case) 200mV / 2.5mA = 80 ohms with a typical value being 50mV / 2.5mA = 20 ohms.

If you want to drive 3mA then the closest you will get to the rails is going to be between 60mV and 240mV.

(There are known ways to get down to zero such as providing a negative power supply of sufficient magnitude).

That means that the lowest voltages out of the DAC (assuming 0V is it's lowest output voltage and the buffer is on a single positive supply) will lose at least 20 least significant bits (counts) of resolution.

Other devices may be more suitable in this application and there really is no substitute for narrowing the list down and then doing a pretty deep dive into the datasheets to see which device is the most suitable for a given application.

The details of the application specific data are not going to be in any of the parametric tables at the various vendors (that is what the datasheet is for).

So we really cannot narrow the search down further before having to look at the datasheets (thankfully now that is not nearly as tedious as looking through the physical databooks - I remember those times well!).

For this particular application (and assuming I can live with not getting closer to the power rails than &lt; 100mV) I would probably choose an old favourite - the AD8615 (there are many devices that would be suitable; this is simply one I have used in this sort of application in the past).