I'll try and answer your questions.
1. The vaccine was tested before it was introduced. It is the opinion of Babyjabs that this testing was inadequate. I think it's true that the initial testing wouldn't have picked up rare or long-term side-effects - but the studies that have been done since then would.
2. Yes, you have to wait between vaccinations. The Babyjabs website says "We recommend between six months and one year between each immunisation" so kids would be unprotected against mumps & rubella for at least 6-12 months. In fact, they don't offer mumps vaccine - so kids are just unprotected full stop when it comes to mumps. I've criticised Halvorsen (their medical director) for this before on my blog.
3. I'm not sure a study can exclude that possibility, but some of the papers they cite actually show lower risk of autism / IBD in kids vaccinated with MMR. Lower. Risk. If the risk is lower in MMR-vaccinated kids how on earth can MMR be causing autism and IBD??
Richard Halvorsen is an anti-MMR doctor who wrote a book called "the truth about vaccines". You can read what I think of him here:
http://jdc325.wordpress.com/category/richard-halvorsen/ (including some posts on his book).