What is the meaning of: merging with Brahman after Moksha?
According to Shankaracharya, the individual self (Jivatma) literally becomes Brahman. But according to Ramanujacharya, the Jivatma acquires a nature similar to Brahman, but keeps its own separate identity while having the knowledge that Brahman is its Antaryami:
The consciousness of the released soul therefore expresses itself in the following form: 'I am Brahman, without any division.' Where the texts speak of the soul's becoming equal to, or having equal attributes with, Brahman, the meaning is that the nature of the individual soul--which is a mere mode of Brahman--is equal to that of Brahman, i.e. that on putting off its body it becomes equal to Brahman in purity.
This is what it means to "merge with Brahman" according to Ramanujacharya.
Is this kind of life eternal?
Yes it is. The last sutra of the Brahma sutras is:
anAvrtti shabdAt, anAvrtti shabdAt
Non-return, according to Scripture; non-return, according to Scripture.
Which means the released soul will not return to samsara; it will be in the state of moksha for eternity.
... without body?
The released soul has a choice to be with or without body, and change it whenever it wants to.
Reverend Bâdarâyana is of the opinion that the Released may, at his liking, be with or without a body.