how to get same framing tonight as last night?

If you plate solve an image with the ASIair it provides the coordinates and the rotation angle. You could make a note of both those on the first night. On the second night you input the coordinates, slew the telescope and then plate solve again. You can then repeatedly adjust the rotation angle and plate solve until the angle is right. If you didn’t note down the coordinates and rotation on the first session you can get this info by uploading your image to various sites like Astrometry or Telescopius to platesolve.

Agreed with @andresch , and once your scope navigates to the center of the previous night's image, if necessary, a message will show on your screen informing you that the angle of the current framing needs to be adjusted.  The text (at least on my screen) is garbled, but if you tap the center (different colored text), you will be shown both views and the amount CW or CCW you need to turn your camera to to align the current view to the previous night's image.  Once you make an adjustment to your camera angle, you can refresh the screen to monitor your progress.  I don't think I've ever gotten it closer than .2 degrees ....

I used to capture in Nebulosity, before i switched to NINA. In Nebulosity, you can load an image, place three fiducial markers on top of three prominent stars in your image, and then frame your life view to these fiducials. If you didnt touch the camera, rotation should still be perfect.

This is only a digital version of Francois' marker approach, it allows zooming in, though. If i remember right, there is a free version of Nebulosity.

Use the goto option mentioned earlier and take preview images where the stars are visible. Rotate according to how your images from the previous night were (check for stars in the corner of the image). This may take a couple of iterations before it works.

I use a digital level (like this one) to record the rotation of the camera. For instance, at the moment I am imaging M31 with an APS-C sensor and I have it rotated 12.5 degrees counterclockwise to allow the galaxy to span the widest dimensions of the sensor, from corner to corner. Before I mount the telescope, I sit it on a flat surface, zero the digital level to that surface, and then place it on the flash hotshoe of my DSLR. I rotate the camera until it reads 12.5 degrees on the level, and lock it in that position.

For this to work on a dedicated astronomy camera, you'd need some sort of zero-reference for the level to sit on - perhaps some printing on the back of the camera, or one of these. But the digital level has been so helpful, and removes the need to platesolve and check.

CS!