In relation to stampduty, where a first time buyer buys with a second time buyer, the first time buyer loses their exemption. However in your case you are actually buying as a first time buyer, but I see from your other post that your partner is already the owner of the property ( at least half of it). In those circumstances, what is happening is actually a transfer of half of the property to you, and therefore no secondtime buyer is involved in the transfer as such. There fore you may well qualify for first time buyer relief on the half in transfer.
I don't know the answer in relation to 100% mortgages.