Hi Jolan good clues as always- here are my stabs. Glad you are on the mend.
1. Perceptively sigh when troublesome elderly cat’s put out (5-9) Clear sightedly (anagram of sigh elderly cat)
2. Misleading two pelicans? (6-8) Double crossing (play on words ‘pelican crossings’)
3. Find second class at each end of the First Lady's train (5) Level (second letter of class at the beginning and end of EVE (first lady). Level is a synonym of train
4. Mercy shown by man revealing old defensive weapon (12) Quarterstaff (quarter as in mercy and staff as in man)
5. State he would notice (4) Heed (sounds like he would or he’d and heed as in listen or notice)