From a monthly outgoings perspective it stacks up for you as a mortgage of €108,000 would cost about €750 with life insurance on a 20 year term. You would also have to factor in costs such as property tax, insurance and maintenance that you do not currently pay. What you pay in rent now should cover all of this. Unfortunately this does not mean that the affordability calculator that a bank uses would agree that the loan is affordable to you.
In terms of savings, you would want to be able to pay the deposit, legal costs and do whatever fit-out and furnishing is necessary for a house. It would also be advisable to have some form of 'rainy day' savings. As your savings do not cover a 10% deposit on a house of 120k, this alone is likely to impact a bank's willingness to lend.
The issue with the nature and length of the employment contracts is a challenge but can be overcome when other factors such as savings, the loan to value, level of earnings etc. are in your favour.
I would suggest that your priority should be to increase your savings.