There are a lot of rumours and panicking about so called "shadow banning" (SB) on Twitter. So what is shadow banning? How can you prevent it? How do you know if you are? How can you get un-banned?
There are a couple of important things to remember:
1) There is a lot of misunderstanding about what SB is and how it affects you.
2) Twitter hasn't got an official stance on what gets you a SB.
Therefore, everything you read (including here) is either rumours, anecdotal, trial & error or guesswork.
Breaking Twitter's Twitter usage policies may contribute to a SB. It's an effort by Twitter to cut down on spam. The idea is that if someone is spamming or causing others nothing but grief, they get silenced. And they don't know. The disruptive individual keeps going, they don't get any warning they just have their voice taken away.
It seems that if you have a SB the promoters running competitions can still see RTs and still get RT/Like/Follow notification. But they may not be able to see something you have tweeted. Presumably they can see a DM. It may be that only certain tweets are hidden, whereas others are visible as normal. If you have a link to a hidden tweet, you can still view the tweet, it just won't show up in a search.
To see if you are SB-ed you could ask a friend to see if there are any missing tweets, but they'd have to look one by one.
There are several SB checking sites: http://shadownban-checker.xho.bedita.net/ is one. They check whether they can see at least one tweet and one reply made by you. It's difficult to say how accurate they are.
You can also search on twitter for tweets from your username. Type from:username with your username in the search box on Twitter.com. So if you are called @turnipface7, you would search for from:turnipface7.
To un-SB yourself... it seems, at least some of the time, that these shadowings are only temporary. It has been reported that 72 hours seems to be the magic timeframe. Or it may be that sometimes it's more or sometimes less. Some have enquired about becoming an advertiser, and found the SB has been instantly lifted; although others say maybe that Twitter got wise to this.
And finally, Twitter has a track record of trying things out. They tweak things as they discover what works best and what annoys people too much. Like many other things they've done, they will learn from it and hopefully make it work better.