They used a crane in Star Wars, and actually had to open up the roof of the soundstage to do it. (One of my favorite practical shots in the movie.) They did use forklifts for the snowspeeders lifting off in ESB.
Apparently they went back to Cardington in Bedfordshire to film in the same Hangers that they did for the original in 1977
Also why do people keep quoting the Alarm from the trailer as being the “Imperial Alarm” This is also the Alarm on the Tantive (Blockade Runner) right?