My private key is not recognized. I am trying to retrieve my private key by debugging the address that was used for sending bitcoins to my wallet in the Bitcoin Core App. However, when trying to import this private key in another app it does not recognise it.Do you know where the problem might be? 
(Another thing is that I do not have enough space to sync my wallet, can this cause the issue?!) Thanks for help.
There's many different types and formats for Private Keys. 

For example, a single address private key(WIF) should look like:

5HueCGU8rMjxEXxiPuD5BDku4MkFqeZyd4dZ1jvhTVqvbTLvyTJ


other types: 


Hierarchical Deterministic (HD) Wallet Keys



  Wallet software may use a BIP 32 seed to generate many private keys and corresponding public keys from a single secret value. This is called a hierarchical deterministic wallet, or HD wallet for short. The seed value, or master extended key, consists of a 256-bit private key and a 256-bit chain code, for 512 bits in total. The seed value should not be confused with the private keys used directly to sign Bitcoin transactions.


Example:

xprv9s21ZrQH143K3QTDL4LXw2F7HEK3wJUD2nW2nRk4stbPy6cq3jPPqjiChkVvvNKmPGJxWUtg6LnF5kejMRNNU3TGtRBeJgk33yuGBxrMPHi


Mnemonic phrase
A mnemonic phrase, mnemonic recovery phrase or mnemonic seed is a list of words which store all the information needed to recover a Bitcoin wallet. Wallet software will typically generate a mnemonic backup phrase and instruct the user to write it down on paper. If the user's computer breaks or their hard drive becomes corrupted, they can download the same wallet software again and use the paper backup to get their bitcoins back.


Base58 Wallet Import format


  When importing or sweeping ECDSA private keys, a shorter format known
  as wallet import format is often used, which offers a few advantages.
  The wallet import format is shorter, and includes built-in error
  checking codes so that typos can be automatically detected and/or
  corrected (which is impossible in hex format) and type bits indicating
  how it is intended to be used. Wallet import format is the most common
  way to represent private keys in Bitcoin. For private keys associated
  with uncompressed public keys, they are 51 characters and always start
  with the number 5 on mainnet (9 on testnet). Private keys associated
  with compressed public keys are 52 characters and start with a capital
  L or K on mainnet (c on testnet).



Mini private key format Some applications use the mini private key format.



  Not every private key or Bitcoin address has a corresponding
  mini private key - they have to be generated a certain way in order to
  ensure a mini private key exists for an address. The mini private key
  is used for applications where space is critical, such as in QR codes
  and in physical bitcoins. The above example has a mini key, which is:
    SzavMBLoXU6kDrqtUVmffv


You should know which private key they're asking for and you are sending the correct one. 

Importing private address key (WIF) command should be like that:

importprivkey yourPrivateKeyInWalletImportFormat "TheLabelThatIWant"