Free body diagrams

Sketch the object alone, replacing each contact with the force that contact exerts on the object. Gravity acts vertically down with magnitude $mg$. A rope pulls along its length, away from the object. A smooth surface exerts a normal force perpendicular to the surface. Friction, when present, lies along the contact and opposes relative motion or the tendency to slip. Put forces at their relevant contact points if rotation matters; for particle-like translation problems, their directions and magnitudes are the priority. Do not add a force that the object exerts on something else.

Choose axes and mark their positive directions before writing equations. If a pull $T$ makes an angle $\theta$ above the positive horizontal, its components are $T_x=T\cos\theta$ and $T_y=T\sin\theta$. Components pointing against a chosen axis are negative. Add all components algebraically, rather than adding the magnitudes of slanted forces. For instance, a vertical force cannot directly change horizontal acceleration, although it can change the normal force and therefore the available friction. An FBD should contain the original forces; component arrows can be shown separately if they improve clarity.

For a body at rest or moving with constant velocity, $a_x=a_y=0$, so $\sum F_x=0$ and $\sum F_y=0$. For an accelerating body, use the measured or unknown acceleration in $\sum F=ma$ along each axis. If a crate stays in contact with a horizontal floor, its vertical acceleration is zero even when it accelerates horizontally. The normal reaction is whatever the vertical balance requires, provided it stays non-negative. It is not automatically equal to $mg$, particularly when another force has a vertical component.