Are bitcoin transactions guaranteed unique?
Yes. Each transaction references an output of another transaction, and that output is unique.
Can they be manipulated?
Manipulated in what way? You can add arbitrary data into a transaction.
Can you determine in advance a transaction Id?
Usually no. This is because the signature(s) in a transaction use random nonces and that randomness then makes the txid not predictable.
Been reading bitcoinwiki on Transaction, but could not find the answer we are looking for.
With the extensive knowledge base here on this forum, these should be simple questions.
If there are better documents to view, this would be helpful also.
Take a look at the documentation on bitcoin.org.