Basking is sitting or lying in warmth, enjoying it. You can also bask in something pleasant, as in "she was basking in the attention". Lizards like to bask in the sun because they are cold blooded and the sunshine warms them up.
Begging is a way of asking for something to be given to you, in a humble, pleading kind of way. The dog in the picture is begging for food.
You behave when you act in a way that other people expect you to act, depending on the situation. The puppy in the picture is being well-behaved and is sitting quietly.
Someone or something belongs in a group if it is a member of that group. Something belongs in a place if it is meant to be there, for example "the plates belong in that cupboard". Belong can also mean ownership, as in "that dog belongs to me".
You bend something when you change it from being straight into a curve. Someone has bent the metal bar in the picture.
Something is billowing if it is rising up or puffing out in a big surge, usually from the wind. sails and flags are often seen billowing.