Can an object move with an constant velocity if the forces acting on the object are in separate directions?

It seems like you haven't fully internalized Newton's second law, F=ma. If I had to guess, the reason you know that (1) and (3) can't be stationary but think that it's possible they could travel at a constant velocity is because your gut feeling is that F=mv, i.e. that if "both forces were constant throughout a time interval ... the velocity [would] be constant." It's perfectly normal that this is your gut feeling - heck, Aristotle and everyone (that we know of) thought so for thousands of years until the 1600s, when Galileo/Newton discovered differently. The reason that this is your gut feeling is that we live in a world filled with friction (which is a force). When you look at that diagram, you're probably thinking "something is pushing that way and something else that way," but without you knowing it your brain is filling in "ps. there is friction, as usual, pushing in the opposite direction." This gut feeling that nearly everyone develops is plain wrong. If you want to overcome this, here is how. You need to convince yourself that your intuition is wrong and be constantly aware of this potential error your gut feeling can make. Through practice (i.e. study, thought, problem solving) you have to git rid of that persistent lurking feeling of "ps. there is friction." In short, you must be cognizant of this flaw in your intuition and refine your understanding via practice until you develop a corrected intuition.

for a body to be in constant velocity no net external force should act on it in any http://axis.so in case 2 there is no force in y -axis but if F1= F2 there is no net force in x axis so overall no force while in 1 in y axis there will always be a component of f1 in y -axis. in 3 also in y -axis u have f3+fi x-component.while in 4 f3-fi y-component and f2- fi x component cancels total force

In a frictionless environment the only situation that would lead to the object having a constant velocity is if there is no "net" force in any direction. In other words, all of the forces have to be able to cancel each other out. If the answers to a & b is suposed to be 2 & 4, then the question is written incorrectly: It should specify that the magnitudes of the forces cannot be zero, otherwise all four options could lead to a stationary object when all the force magnitudes were set to 0. Because it is not specified that the forces cannot be set to zero the correct answer to part a) is 1, 2, 3 and 4. The question should also have specified that the magnitudes of the forces cannot be negative, otherwise block 3 is identical to block 4 when the magnitude of F_3 is negative. Because the question doesn't specify that the magnitudes cannot be set to a negative value, the correct answer to part b) is 2, 3 and 4.