Q1 if your partner agrees, you can take an additional advance as a deposit for a new property. Q2 you will have to pay the additional dwelling supplement. See guidance note, particularly foot of p45 and top of p46 https://www.revenue.scot/sites/default/files/LBTT%20Additional%20Dwelling%20Supplement%20Legislative%20Guidance%20-%2016%20March%202016_0.pdf#page45 Q3 you are not eligible for help to buy as you are not a first time buyer.
You would have to transfer the property to your partner so as to avoid the additional LBTT and to qualify for help to buy you would be restricted to buying a new house from a builder. Those are the only circumstances where you could apply for help to buy. If you were able to satisfy both criteria you could proceed. Are you able to do so?
The main thing is that the mortgage lender would have to be asked to consent to the transfer and remove you from the mortgage. That means that your partner would have to be financially able to take on the mortgage and satisfy the lending criteria. That should be your first enquiry. You may want to enter into an agreement whereby you would preserve your interest in the house until a defined date in the future.
You could, for example, enter into an agreement, whereby as and when the house is sold you would get so much of the sale proceeds notwithstanding that the title has been transferred to your partner. Something like that could be time stated, eg, when youngest child finishes school. This is just an example of course.