1. Rent a car. IF you really are opposed, then use a taxi, but really, rent a car.
2. If you have a car, then you can partly 'justify - it by picking up a few groceries or eating a few meals offsite (arrival, departure and transfer days). You can even combine eating offsite and picking up a few groceries if you stop by the Whole Foods. Though it's a bit pricey for groceries.
3. We prefer to Universal first. Great place, but it's not WDW. I've tried doing it on the last day, too. Neither is wrong.
4. We usually spend one day at Universal. But the last few trips we've only done IoA. Three is probably a good number of days. In my opinion, WDW has more very good rides, but a few of Universal's rides surpass anything WDW has to offer. Spiderman, HP, and the Mummy are all amazing. I was SO hoping the Lm would be on par with one of those. too bad. Also, Universal -compared to WDW - tends to take things a little further. Where WDW dribbles a little water, Universal likes to drench it's guests. Wear a bathing suit under your clothes, and carry as little as possible.
5. Three days at Universal is going a bit slow, but three days at WDw means skipping lots of stuff. Better, IMO, would be two days at Universal, and five at WDW - or four if you are staying with the total you days you've listed.
6. no matter what, you will lose time on the day you transfer. the two places are at least half an hour drive apart, plus if you are changing hotels you'll need to pack up and check-in. If this is a summer trip, you could easily spend that day doing slow check out- pool- and either DTD or Citywalk.(or maybe one of the other water park/mini golf type things. If you are focused on spending that day in the parks, then really a car would be helpful.
We've done offsite for Universal, and it can be done. Then again, lots of folks like WDW offsite too. I prefer onsite for WDW. My preference is to do a split stay (part onsite at WDW, part near Universal- on or offsite) but you can also have a great vacation staying at just one hotel. If you are doing just one offsite hotel though, you really want a car. The shuttles that most hotels offer only run like once an hour - at best. Many are far less frequent. no matter where you stay, time = money. Free shuttle buses = huge time loss. A trip to Orlando is $$ - even at the value resorts- don't waste that effort waiting on shuttle buses. If you really don't want a car, the ME bus is okay, but consider paying for taxi's.