Weapon of the sea, undented, times x or y minus the first, reversed.
A weapon of the sea is a trident, undented gives tri which means 3. x and y refer to an axis, minus the first letter xis then reversed is six. 3x6 =18.
3-4 triangle complete.
As found by @Omega Krypton 3,4,5 triangle by Pythagorean theorem.
A bucky lemur nun.
Anagram for 'an unlucky number' which is 13.
Shakespearean poem less nonagon's sides.
As stated by @AHKieran a sonnet has 14 lines and a nonagon has 9 sides therefore 14-9=5.
Krypton minus vanadium.
Krypton's atomic number is 36, Vanadium's is 23, so 36-23 = 13
In, at, of or pi.
Best guess for now is first two digits of pi since each word is two letters which gives 3 and 1. 3 -1 is 2 possibly or 3+1 is 4? Likely gives a two.
Flags in tic-tac-toe position 3 and 8.
As found by @JR_M using semaphore flags you get 5.
is 18 in binary.
Palindromic animals slammed in a net plus backwards epsilon.
A palindromic animal is a ewe, an epsilon backwards looks like a 3. Not sure from here with this one. net backward is ten, 10+3 gives 13.
Neutrons in carbon isotope with 20-minute half-life.
Carbon-11 has a 20 minute life and has 5 neutrons.
Knights and queens on a starting chessboard.
there are 6 (4 knights and 2 queens on a chessboard to begin). Also possible it is referring to the rank or file of there positions.
$(2.5x^3 - 28x^2 +163x-6374)'''$
The 3 apostrophes indicate third derivative of the equation which is 15.
rot13 on it gives eighteen.
If you take all the numbers: 18-5-13-5-13--5-13--5-6-15-18 and translate using a1z26 you get REMEM_ER_EFOR. If I had to guess the 6th letters is a B and then the 9th letter is either a B or an M. If they are both Bs it is a misspelling of remember before, if the second letter is an m it gives remember me for... which is part of a lyric in fall out boy's song, centuries.