1. The machine is movable.

Question

2. The machine is unmovable.
3. The machine is immovable.

(What is the opposite of 'movable'? Is it 'immovable' or 'ummovable'? Are the three sentences all grammatical?)

Answer 1

The three sentences are fine.

Both of those antonyms for "movable" are fine, too:
http://thesaurus.com/browse/movable?s=t