Does a chord like C11 contain (apart from 1st, 3rd, 5th) the 7th and the 9th? Or I can just play the 3rd, 5th and the 11th and the root?
I have the same question with chords like C9 and C13.
Strictly speaking, chords are stacked, as in 1,3,5,7,9,11,13, with all notes played. However, on some chordal instruments, there is not the facility to play all notes simultaneously. You're fine with, say, a keyboard, but a guitar with 6 strings ? So certain notes can be omitted. To make , for example, a C11, it can use the C (root note, without which it's no C chord), the 3rd (defining maj. or min.), the b7th and the 11th, which is essentially a 4th up an octave. The 5th is sometimes left out, as it doesn't define the chord. The 9th isn't always in, but can be if there's room.
If you play 11 without the 7th, it becomes "add 11" or "add 4" - not, note, the same as "sus 4".
With 9th, you need , again, root, 3rd (maj/min.), 7th (of some sort) and 9th (of some sort).Obviously, on guitar, there's spare strings to include the 5th as well).
13th often sounds just fine with 1, 3, 6, and 7, again using the appropriate 3 and 7, usually maj.3, maj.6 and b7. Keep 6 and b7 an octave apart, otherwise they will clash.
If these are guitar chords, care needs to be taken to voice in a harmonious way, hopefully with the 9, 11 or 13 an octave at least above the root (bass) note played.
You can find a large list of chord names and formulae on the question What determines a chord's name?
Including 9, 11, 13, and how to work them out from their name