Hard Puzzles 

Workings

Hint
This is a well known nursery rhyme.

Answer
AJCTA.

These are the initial letters from the nursery rhyme 'Jack and Jill went up the hill'. The letters represent 'and Jill came tumbling after'.

Workings

Hint
The code has just four letters, A, B, C, and D. Each letter encodes 5 different letters.

Answer
I think, therefore I am.

Reasoning
A represents a, b, c, d, and e.
B represents f, g, h, i, and j.
C represents k, l, m, n, and o.
D represents p, q, r, s, and t.
E represents u, v, w, x, and y.

Workings

Hint
This is quite a common representation of the alphabet.

Answer
L.

The last letter from hoteL, which is H in the phonetic alphabet, alphA, bravO, charliE, etc.

Workings

Hint
One of answers involves royalty.

Answer
Prince, princes, princess.

Bra, bras, brass.

A similar change is care, cares, caress, but these are not nouns.