Do I need a telescope to see meteors?
No. Meteors move fast and can appear anywhere in the sky, so your eyes are the best instrument. A telescope or binoculars would show only a tiny patch of sky.
It surprises many beginners, but the ideal equipment for meteor watching is simply your own eyes. A meteor flashes across tens of degrees of sky in a second or two, usually without warning. A telescope shows a patch of sky smaller than the full Moon, so the chance of a meteor crossing that small field during your session is very small. Binoculars are only slightly better. Your naked eyes, by contrast, take in a huge area at once.
What helps far more is a dark sky and dark-adapted eyes. It takes 20 to 30 minutes for your eyes to reach full sensitivity in darkness, and a single glance at a bright phone screen can undo much of that. Use a torch covered with red film or a red light, which disturbs night vision less. A comfortable reclining chair or a mat, a sleeping bag or blankets, and a warm drink make longer sessions pleasant, and the longer you watch, the more you will see.
Optical aids do have uses. After a bright fireball, a glowing trail called a persistent train sometimes lingers for seconds or even minutes, and binoculars can show it twisting in the upper-atmosphere winds. Many enthusiasts also use a camera on a tripod with a wide-angle lens, taking long exposures to catch meteors, and networks of automatic cameras across the UK and elsewhere record fireballs every night to work out their orbits.
If you are watching around dawn or dusk, never point binoculars, a telescope or a camera viewfinder anywhere near the Sun, and never look at the Sun directly: it can cause permanent eye damage in an instant. For meteors, wait until the Sun is well below the horizon and simply enjoy the whole sky.