Copy all important files into a folder, uninstall MC, reinstall MC, put important files into reinstalled MC. If that doesn't work it may be that a key on your keyboard is stuck, or that you're account on the computer doesn't have security set up correctly.
I think you may be missing core mods. For instance: Superheroes Unlimited requires the Legends Core to run. otherwise, it may just be that the mods need a later (or earlier, but it's unlikely) version of forge. And if neither of those work, try installing Java 64 bit, that's how I fixed my servers.
It looks like you may be missing key mods to run other mods. e.g. MalisisCore is required for any Malisis mod. And if you are using a modpack, you may need to troubleshoot. Try reinstalling the modpack, or changing the settings on whatever you're launching it off of to account for errors. Or another possible issue is that you're not using 64 bit java, in which case use this link https://www.java.com/en/download/manual.jsp to download it.
You really can't without using a server hosting service. There are a few free ones, but generally they don't run very well. If you really want a good server get a subscription to a hosting service like MCProHosting (But their servers aren't great, that's just an example)