1. The size of the filter does impact the image but not in the sense that the 2" is better than the 1.25" version. It is related to the size of your sensor and the speed of your telescope. If your sensor is small and the telescope is say F5 or slower, then you can likely just use 1.25" filter - cheaper and no impact on quality. If the sensor is larger or you have a fast telescope then you will need the 2" filters, as the smaller ones will cause excessive vignetting.
2. 35nm would not be suitable for good deep sky imaging, 7nm will give nice contrast and is what I use.
3. You often get what you pay for with filters, Baader would be decent. I have some Optolong Ha Oiii Sii filters that I like also, and seem very comparable to Baader.