thieving pads

In Allegro PCB Editor, its present under the menu Route> Gloss>Parameters/Design/Room/Window/Highlighted/list, Here parameters are for making the settings rest are the option how user wish to execute the command.

Under parameters > Fillet and tapered trace is selected to make the required settings.

In Allegro command window as well this can be executed type in

add fillet

Command uses current Glossing/Fillet parameters

How to apply this manually a selected pin? Is it possible to demonstrate it?

How to apply this manually a selected pin? Is it possible to demonstrate it?

After setting the parameters you can drag select the canvas if you wish to perform on multiple pins/nets if its individual pin you may click on the pins.

Is it possible to change the direction of teardrops? It's through trace. Or should it normally be like that?

Teardrop follows the trace, by design.

I am informed by my team that there is not nothing to do with teardrops/filet and tapered trace. Basically it is enlarged pads in the bottom layer that will help to "catch" any excess solder paste so that solder shorts does not occur as easy. It will be applied to last pin of the component. have any idea how to implement that?

There are two types of Thieving, Copper Thieving and Solder Thieving, Copper thieving is used for Copper balancing in the PCB and Solder thieving comes handy in the reflow process of soldering where the last pad is provided with extra pad area or separate pad at the same distance to steal the excessive solder (placement also plays an important role generally odd angle placement is avoided). Some users provide fillet for better connectivity, manufacturability and re-solderability such that the traces don't have broken joints while rework.

The first image you shared is of Fillet/teardrop in Allegro my response was in line to that.

In your case if you wish to provide solder thieving pads you may provide the same in the footprint by providing extra pad with soldermask open.