Those letters spell celebration.
No word contains only the letters f t and h. A word that contains all 3 in that order is faith.
There are no words that contain all of those letters.
quarts
Rearranged, it spells tantalize.
The word "multiply" contains the letters m, u, l, t, i, p, and y, which totals 8 letters. The word "product" contains the letters p, r, o, d, u, c, and t, totaling 7 letters. The common letters between "multiply" and "product" are p, u, and t, which are 3 letters. Thus, the fraction of letters in "multiply" that are also in "product" is 3 out of 8, or 3/8.
Upstage.
Saltwater is a word. It contains the letters AWATELRST.
Ditty, ditsy, dotty
Unfortunately, none in the English language. The largest word with IIVAU, is VIA and with the T added, it's VITA or VATU. There are none with 5 letters.
One word that fits your criteria is "distant." It starts with the letter 'd,' ends with 't,' and contains seven letters.
Mistletoe.
The word you are looking for is "defeat." It contains all the letters d, e, f, o, t, and u, along with the letter b, forming a coherent word.