Hi
1) Honeyfund doesn't take any fee as long as you stick to the standard service. I preferred paying $29 to get rid of ads from our registry and have a nicer-looking website, but you can definitely do it for free if you're ok with plainer looking website with ads. Paypal takes about 3% of the gift. Since we were not sure when we can go to honeymoon, we didn't want to/couldn't use the Disney website (in fact, we married last October and are finally going go on our honeymoon this September

). The flexibility of Honeyfund was really helpful for us. If you want to avoid any fee at all, you can just opt out the paypal/credit card option and ask the guests to pay in cash or check.
2) We didn't do a bridal shower, so I can't help you there, but I think you can ask whatever you want to your guests; it's your wedding. Most of our guests didn't bring any physical gifts on the wedding date, but paid through the paypal to our account before the wedding at their convenience, and some brought cards on the wedding day, which was really sweet. I also enjoyed the coupon and the message they can send together with their gift payment.
I was worried about this unconventional gift registry, so we did ask around our family, friends, and relatives first to see if they are comfortable. But since we were already living together before our wedding, it made the most sense to do it this way. We also told them no gift is fine, since it was a distant wedding, but surprisingly, thanks to our generous guests, the gift we got will cover our one week honeymoon, staying at Grand Floridian, and we're really grateful