There should be shuttles meeting flights at the airport to transfer you to El Chalten.
There are also a few companies that run buses. There is usually 3 (not completely sure) buses a day from El Calafate to Chalten. They swing by the airport but they go at 8am, 1pm, and 6pm. Which doesn't help you too much. It should be about 20 USD or 800 ARS.
A shuttle from las Lengas is about 40 USD one way.
Obviously a hire car is going to be more expensive. But it will give you a bit of freedom - though you don't need much in Chalten. Though it might be a good option when you go to the glacier - so you dont have to take the bus. A quick search for those dates and the cheapest car is about 350USD.
A check in time of 9pm would be fine. Most places have 24h check in. Just let them know when you arrive. You could take the 6pm bus and be in by 9pm.
1) Is a car worth it. You don't really need on in El Chalten. The trails all leave from town. Its not really worth it. Though the Bus from FTE to Chalten won't get you in til about 4pm. Youd be able to do a nearby hike like Condores but nothing much.
2) I haven't done the ice trek.
3) Theres two main treks - up to Laguna De Las Tres and to Laguna Torres. I would also highly recommend going to Laguna Sucia (the trail offshoots from De Las Tres) but you will need to get a permit from the Parks office. Do De Las Tres on your full day. Then get up early (pre sunrise and hike out to Laguna Torre and back. I can usually get out to Torre in about 1.5-2hours with a heavy backpack. Both hikes are relatively flat-ish (bar the first few kms and the last km of de las tres).
