I have always used buoyant force as acting upwards in any problem related to fluid mechanics that I have solved. Also, if we push a mug down a bucket of water. It rises up, always, not diagonally even if it is pushed diagonally inside. Does buoyant force always act upwards? If yes, how is it consistent with Newton's Third Law?
The buoyant force is directed against the pressure gradient, that is in the direction that the pressure decreases. If you define this direction as "upwards" then the buoyant force is due to the contact force difference between the lower (higher pressure and force) and upper (lower pressure and force) parts of the body. Regarding the third law, if the buoyant force is acting upwards on the body, the reaction is downwards in the fluid.
If your frame is accelerated this also causes a gradient of pressure. Check this video to see the diagonal buoyancy forces in action. This happens because the air inside the car has mass therefore inertia. When the car accelerate, the air gets denser in the direction contrary to the acceleration. This causes difference of pressure therefore a net force on the balloon.
Buoyancy refers to the upward force exerted by a fluid against the weight exerted by an immersed object. The pressure difference between the top and bottom portion of the submerged object in the fluid causes this upward force. The pressure is the normal component of stress. That is, pressure is the normal force acting per unit area. Hence the force due to the net pressure acting upwards will be directed upwards through the center of gravity of the submerged object. The submerged object will have a force exerted downwards, normally, which is the weight of the body. The body displaces through the fluid for some distance until, the force on the body is balanced by the force due to the pressure acting on it upwards. At this point, the body cannot move further. When the applied force is released, there causes an unbalance on the immersed object and to counteract this, the object has to decrease the pressure by going up. Everything seems to be obeying Newton's third law.