I can't, because it didn't sync till the end ( lack of space ), so I backed up wallet and purged bitcoin core.
Bitcoin Core does not need to be synced in order to dump the private keys. You can start it and dump the private keys before much syncing happens. You can also enable pruning mode which will significantly reduce the amount of space required. Pruning means that it will delete most of the blockchain once it has downloaded and verified it.
Can I import that wallet.dat in new Bitcoin core if I install it and sync it, and if I have to, how can I recover wallet ( if it's corrupted ) ?
Just put the wallet.dat file in the datadir and the wallet will be used. Your wallet is not likely to be corrupted.