Can my character cast the spell Haste on himself or can it only be cast on another character?
Yes, you can
The spell merely requires a willing creature you can see within range.
And, as per the rules of spellcasting, you are indeed a willing creature. So unless the spell specifically states a creature other than yourself, then you can cast Haste (etc) on yourself.
If a spell targets a creature of your choice, you can choose yourself, unless the creature must be hostile or specifically a creature other than you. If you are in the area of effect of a spell you cast, you can target yourself.