Travelling to different biomes and exploring the map

I'm new to Minecraft. I've built an enormous base near where I spawned, in a normal field and trees type biome.

I only just learned there are different biomes. I want my farm in my base to have every type of crap and animal.

Is there a fast way to travel between biomes? Doesn't seem feasible to just run and run in a single direction. I'm in survival mode and don't want to die. And definitely don't want to make a bed and be stuck somewhere without being able to get back to my base.

I want to find a jungle to get the pumpkins and melons but can't find it anywhere near my base.

Is every Minecraft map the same or is every server of Minecraft a unite map generation? Are biomes always in the same coordinates?

Is using coordinates and teleporting considered cheating? Can I still get trophies if I use teleporting to get around? I'm aiming to get all trophies.

Could use a fast way to move around the map to different biomes