Once again, there is a lot of misinformation about using PPC.
Pretty much all the major ad networks have more or less the same rules. I suggest using Adwords and follow their policies. If you do, you can't go wrong with any other.
The reason people get banned is not following policies. It has nothing to do with promoting CB products.
Squeeze page: not allowed. The definition being a page where you ask for email or other information before being sent to the offer. You don't get banned for this, your ads simply are suspended until you fix the issue. However, if you keep repeating over and over, they'll ban you since in their view, you are not the type of advertiser they want.
The solution is to have your own sales page but don't send your visitors to the merchant's sales page. That's called a bridge page and not allowed. A "Buy now" button that goes to another sales page is not a buy now button. Instead, send them where it is expected, to the checkout.
The alternative solution is to send clicks directly to the merchant offer. The caveat there is that THAT page has to follow all policies as well. Now and in the future. Otherwise, that campaign will be suspended until the page follows the rules. Since you don't own that page and can't make changes, that's a problem. I can't confirm but I've heard of an entire account being suspended because of this. The solution is to directly promote offers only where the page follows all the rules and should follow them in the future, what I call "safe" affiliates. Unfortunately, most CB products I've seen would not. Read and understand the policies. Failure to do so is what got many affiliates in trouble using Adwords.
>> ANY one page website = ban
Not true.
>> ANY website promoting product without having a full checkout for purchase on the same website = ban
Not true.
>>ANY review website = ban
Not true. Again, review and understand the polices. A lot of review websites I've seen have bridge pages. You don't get banned outright for this, simply get suspended until the issue is fixed. But if you continue insisting on breaking the same rule over and over, you will get banned. Think of it as a three-strikes and you're out rule.
>>ANY website collecting information without a need to = ban
Again, not true. Yes if you are talking about a pure squeeze page (ads suspended actually unless you keep repeating the same offense). No if you do it properly, that is, not simply collecting information.
There is no problem promoting a weight loss product for example as long as it's done right. This niche is affected by a few policies. First, you can't use misleading terms or unrealistic expectations. Saying that the product will let you shed 20 pounds in a days is unrealistic and that would not be approved. Any such product using ephredrine or any of a hundred other drugs on the list would not be approved.
Read and fully understand the policies. If there's any doubt in your mind, get clarification. If you are still not sure, don't promote that product.