Hi Shirley,
I could imagine that with a thickly applied shiny oil paint might show a reflection of the tube nearest it. In that case the cloth may help, but I speak from theory, not experience.
Yes
Yes, 2 are needed for a more even spread of light, the illumination diminishes rapidly with increasing distance, so don't have them too close, hence the suggestion of 45 degrees to the picture.
Here's the idea, but you'd turn it on its side so the painting and lamps are vertical I guess (and larger of course). Note the shades to prevent the light hitting the lens (mounted on column).
If you try to get away with one (at top), you'll have a gradient of illumination that would need fixing in post processing (PP). You may not see it by eye, but it will be obvious in a shot.
Although if far enough away that distance to top edge and distance bottom edge is almost equal, it won't be too bad (but will be quite dim), I think this is impractical, hence two lamps needed.
I think I am right in saying that if the lamp to one edge and lamp to the other edge varies by more than 1:1.4 (as a ratio), there will be a stop difference in exposure - someone please correct me if my "head maths" is wonky.
Inside lights, especially if tungsten, yes and also especially if they are bright and/or close to the picture.
If you view the LCD of the picture illuminated and get the histogram on view and cannot see the difference switching the inside room lights off and on, then it should be OK, it's all a matter of proportion.
Cheers,