Interesting question. As far as I know, I have not read anyone having done that before. The question is whether it is possible? But, before you try your efforts on this, have you already tried using the pan-sharpening option? Using the 15 m panchromatic band of Landsat 8 and the rest of the 30m multi-spectral bands you can improve the spatial resolution of Landsat 8 imagery. Is a 15 m pan-sharpened Landsat imagery enough for your desired purpose? Just curious to know the purpose of merging GE and Landsat imagery. What is the aim of your research?

Although, I do not have the answer to your question, I can at least share some of my thoughts. You need to keep in mind that the date of GE Imagery and Landsat 8 imagery which you are trying to merge may not match. Secondly there is also a question of spectral and radiometric resolution mismatch in addition to projection issues between the two sources of imagery. You may also want to put up the question in Google Earth Community webpage.

https://productforums.google.com/forum/#!forum/gec

https://earthengine.google.com/

yes you can if the land cover is protected

Firstly you need to download all available scenes on google earth for your area of study, mosaic it then apply the resolution merge. But don't forget to consider the timing of the google earth images and the OLI image to be the same.

Regards

Yes, by using the color normalized (Brovey) sharpening technique which calculate a numerical matrix of the Landsat image and the google images as a high spatial resolution imagery. Every band of the three RGB bands in the google image is duplicated by a proportion of the high spatial resolution data divided by the summation of the Landsat bands. The function consequently and automatically resamples the three color bands to the google image with higher spatial resolution pixel size using neighbor, bilinear, or cubic convolution. The final image will have the high spatial resolution pixel size.

I am not sure at what resolution (i.e. broad scale or fine scale) but some  images on GoogleEarth are Landsat images.   If you want the aerial photos, you would be better off going straight to the agency and get the appropriate image from them.

If you do take them from GoogleEarth, make sure you properly site the original source of the image.