No, don't leave dependencies.examplemod, that declares dependencies for a mod that doesn't exist
The logo does matter if you plan to open the mod list
All values in mods.toml marked #Optional should be set or removed entirely, do not leave them blank
The mod.toml file looks fine, and so your mod main class... "examplemod.png" doesn't really matter, and as far as i know you can leave [dependencies.examplemod] as it is and your mod should run without problems. I tested this on 1.16.1 and the mod is loading correctly, but you can try to change "examplemod" in the dependencies to your mod ID and see if it loads, i doubt this is the issue though.
Everything Forge is Open Source on GitHub, you can literally see what you're downloading there.
No there are no viruses or trojans in Forge, many virus detectors like to flag executable files made by people who haven't paid to be whitelisted by the anti-virus maker
Can I ask why you set the BACKGROUND_LOCATIONS at the end? Also not sure if its helpful or not but the first screenshot in the controls menu is rendering the default "textures/gui/icons.png" texture in the background, which oddly enough is the file next to the BACKGROUND_LOCATIONS(textures/gui/options_background.png") file alphabetically in the default resources. They are also both declared as finals in AbstractGui. In the second controls menu the rendered background looks like it could possiblly be the STATS_ICON_LOCATION resource from AbstracGui as well