Question

Is it possible in vim to move forward with t and f (or in the other way with T and F), but using words as a parameter ?

Answer 1

What about /word?

It can be combined with operators just like anything else:

the lazy cow jumped over the high moon

cursor at start, d/highEnter:

high moon

Bonus

Also, you might be interested in learning some of the ex mode commands like that:

the lazy cow jumped over the high moon
the hazy cow jumped over the high moon
the noble cow jumped over the high moon
the crazy cow jumped over the high moon

Now enter

:g/azy/ norm! /jumped<CR>d/high/e<CR>

(Note: <CR> denotes C-vC-m for the enter key (^M))

Result:

the lazy cow  moon
the hazy cow  moon
the noble cow jumped over the high moon
the crazy cow  moon

The /e flag achieves inclusive behaviour like with f; To get ’till behaviour instead:

:g/azy/ norm! /jumped<CR>d/high/<CR>

Result:

the lazy cow high moon
the hazy cow high moon
the noble cow jumped over the high moon
the crazy cow high moon