Some investors are waitlisted when so many people apply to invest that the company receives more money than they can legally accept. Instead of reducing the size of everyone's investment, founders may choose which investors to accept and may prioritize those who can help the most. 

You can decrease your chance of being waitlisted by applying to invest early, connecting your social networks, and filling out your profile.

Yes. An equity stake will almost certainly be diluted.

Successful startups host many rounds of financings, all the way to an IPO. For each financing, the startup issues additional stock to the new investors. As long as the value of the company increases with each funding round, this is healthy and normal. For example, the first investor in Facebook, Peter Thiel, originally purchased ~10% of the company for $500,000. By 2011, that stake was diluted down to under 3%, but estimated to be worth ~$2 billion.

Sometimes, when things are not going well, the startup is given the option of going bankrupt or raising more money in a "down round," which means the value of the company decreased since the last financing. This is very bad for the founders and past investors alike; the dilution happens much more rapidly. But it's preferable to the startup going bankrupt and the investors losing everything.

Everything is handled electronically. You sign a contract when you apply to invest. The founder will sign the contract after the fundraise closes. Once the founder signs, you'll be emailed a PDF of the executed documents. You can always find copies of your contracts on your investor dashboard.

For any company currently fundraising, you can ask the founders questions directly on their profile by clicking the "Ask a Question" tab.  

You should receive a notification from the company about your perks once their campaign is closed and your investment is confirmed.