I want to buy a house and take out a mortgage for it. I plan on making this a rental property. However, I want to travel and start my own company next year. If I do that, I won't have a stable income (or one at all). If by next year, I have completely closed a deal, will the bank stop giving me the mortgage?
Once all the papers are signed, quitting your job will not have any consequences for the mortgage as long as you make all the payments on time. If you made any false statements when applying for the mortgage it's possible that the mortgage could be nullified after it closes, but otherwise, it's your obligation, and until you stop meeting that obligation (including any other agreements you made like keeping it insured and not letting it fall into disrepair) no one is going to bother you.
If you have applied for a mortgage and signed paperwork that says you must occupy the property, you could run into an issue if you convert it to a rental.
In the United States lenders use different requirements when determining a loan for a rental property. They also generally want a larger down-payment. If shortly after taking over the property you tell the lender you have a new address, they may want proof that you are still living there. The paperwork you sign will tell you how long you must occupy the property.
There may also be requirements if you are purchasing a foreclosed property; or you are purchasing the property with government assistance.
Changing jobs isn't an issue. As long as you are making the payments, the lender is happy. But if you want to refinance, then they will reevaluate your ability to pay.