Random tunes are basically ideas that you have for a song/solo/riff or whatever . I get most of my ideas from listening to other songs, I just listen to a certain part and think, *that could work*, I then pick up my guitar and start playing something along the same line, making sure it isn't copyright. Hope this helps you a little bit.
Tabs are the best things to be invented in the whole of the music world! It makes it a lot easier to determine what strings and frets will be played in the song. They're aslo a useful way to make notes on songs/solos/riffs and stuff like that, If you wanted to, you could post one of your own ideas. But then it would be problematic because anyone could take it and use it, but it's up to you if you want to do that. Good luck in the long run though.
This kind of picking brings life and balls to a song, but trying to learn sweep picking for the first is a pain . Starting slower on the tune and then picking up speed when you get more confident is usually the best way, using a tune that you've made or have been given would give you an advantage as you know it well. Good luck with it though.