Ok, let me try and answer some of your questions here:
1) I think May would be your best option, but early May. The parks tend to do refurbs on rides anytime from Jan. to the end of April (and sometimes in May, but not as common). They do this to have everything ready for the summer crowds. So, if you go like the 2nd week of May, the odds of running into a ride in refurb is low.
2) Do not stay offsite, see the next question.
3) Stay onsite! Yes the cost of the hotel seems high, however the onsite hotels are as good (and imo better) than Disney Deluxe hotels plus they come with some perks!
Getting to and from the onsite hotels is a breeze. They have a water taxi in Citywalk which will take you back to the hotel that runs all day (until 1 or 2am normally). You can also take a nice walk along the water taxi path which will take you about 10-15 minutes to reach the hotel.
However, the main perk is the Express pass! You can skip nearly every line for nearly all of the rides in the parks! This is not like the Disney Fastpass where you wait for a return time or anything like that. Simply show your roomkey to the team member at the front of each ride and you can enter the "Express" line and you will normally be on the ride in 5 minutes or less. Some rides you might have a short wait (never more than 15 minutes), but the normal line for the ride could be 90+ minutes. It is an amazing perk and WELL worth the cost of the hotel room alone. I don't know how many days you plan to stay at Universal, but with two days and express passes, you should be able to see nearly everything. I would go with 3 or 4 days however to really take it all in.
4 and 5) We used a car service on our last trip and it was amazing. We used a company called
FL Tours. They were right on time picking us up from the airport with a nice car. Whats great is you can ever get a FREE grocery store stop. We used this to grab a foam cooler, some 12 packs of soda and some water, and some snacks for the room. Saved us a lot of money because we just took the water bottles to the park and had soda in the room.
Whats great about this company is they offer a 3-Leg plan. They will pick you up at the Airport and drive you to Universal. Then, they will pick you up from Universal and drive you to the port. Finally, they will pick you up at the port and drive you back to the Airport! For a family of 4, the price for this was $291. Yes it cost a lot, but it is cheaper than renting a car (you have to pay $15 to park at the onsite hotels if you rent a car, plus you would have to pay to park the car at the port).
Another option would be to take a cab, but you would need to research how much that would cost you and having to deal with the pickup and stuff for cabs can be a pain. With any type of car service company (there are a bunch that service the Orlando area and most offer a 3-Leg type of plan like the one I mentioned above) you will have all the details lined up and they will be there at the times you pick. I mentioned FL Tours simply because it is the only company I have had experince with and it was very smooth without any issues. Others might chime in with other ideas for this one as well. There are a lot of options when it comes to getting to and from the airport in Orlando that don't require a rental car.
If you have any more questions, feel free to send me a PM or post here!