It is most likely RNA contamination, indicative of the "moon-shaped" smear. RNA typically appears this way in high concentrations, and due to its single stranded structure, it tends to act differently than DNA in electrophoresis. Unfortunately, I am not 100% sure, but you can confirm if this is RNA contamination by treating it with RNase, and re-run the sample. If the bands disappear, it is RNA.

I do not understand your question. You have labeled the ladder in "bp", for basepairs as if this is a nucleotide gel. You would not use an agarose gel for proteins, you'd want an acrylamide gel (or starch or other). The glowing bands look like nucleotides, not like stained proteins.

What exactly did you load on your gel? Whatever it is, you've loaded way too much, that's why the bands are bending.

Here's info about 260/280 ratios in nucleic acids https://assets.thermofisher.com/TFS-Assets/CAD/Product-Bulletins/T123-NanoDrop-Lite-Interpretation-of-Nucleic-Acid-260-280-Ratios.pdf

And here is info for 260/280 ratios for proteins:

https://trialtusbioscience.com/blogs/protein-corner/interpreting-the-od-260-280-ratio-for-protein-purity

It sounds like you are purifying a protein but suspect DNA and/or RNA contamination. You can treat your protein sample with DNase and/or RNase. But, protein purification should be removing these molecules from your protein during the extraction and purification. Any reason to think your protein binds nucleic acids?