1. It’s possible that it is Powdery mildew the most common disease on this plant. Growing honeysuckle in full sun and proper pruning will help minimize this disease problem. Mildew develops in warm, wet conditions. Exposing your honeysuckle to sun and air will help prevent mildew from developing further or even at all, if you are lucky. Mildew develops in warm, wet conditions. So I believe your pruning will help with this problem, but not sure if it was already there before you pruned. Other help:

Water your honeysuckle from the bottom, not the top. Water that sits on the leaves for hours will contribute to mildew development.

Remove the debris of dead leaves or any infected plant material that you pruned away from the plant. Do not let it sit on the ground near the plant, as the fungus can overwinter in the soil. Throw the debris away or burn it. If you compost it, the fungus can live and infect other plants.

Other honeysuckle problem:  

2.

It may be aphid honeydew, a polite term for insect excrement. Honeydew is an ideal substrate for sooty mold to develop (it is dark not white). Although it is unsightly, sooty mold does no real harm to plants. If this is the case, returning aphids can come due to laying eggs. However, in spring if you see aphids just use a strong water spray to knock them down which helps a lot.

If there is a stickier residue you can control this in late spring before the plants leaf out, apply horticultural oil as a dormant treatment. The oil will suffocate many of the eggs and reduce the population of overwintering aphids. This is NOT dormant oil. Horticultural oil is more refined and less injurious to sensitive plant tissues.

Horticultural oil has the added benefit of being soft on beneficial insects and pollinators because it only affects insects in direct contact with the spray. Once the spray dries, it has no residual activity. Avoid applying horticultural oil to drought-stressed plants. You can irrigate thoroughly the night before spraying if necessary. Also, avoid applying horticultural oil when temperatures are 90 degrees or above or when humidity is very high to minimize damage to plants.

 Now that cooler weather is on its way, applying oil now may not be best. https://extension.tennessee.edu/mtnpi/Documents/handouts/Insect%20and%20Disease%20Control/Horticultural_Oil_Handout.pdf

 Hope this helps.