Does the plenty o biome's mod make minecraft lag?

Yes, only when you're generating new chunks or have a terrible computer. For future reference any large mod that adds a tons of stuff or changes world generation or mob spawning will cause lag. Also the more mods you have (even if they all just minor tweaks) the more it will lag.

That depends on your specs and how much RAM you allocate to Minecraft, Biomes O' Plenty can cause lag issue if you don't have enough RAM allocated to Minecraft

Depends on your computer really, like if its a laptop probably.

Check the website where you are downloading the mod from and see if it has a list of recommended computer specs to see if your computer is powerful enough to run it. After you have installed it, lower all of your graphics settings to test if your computer can handle it. If it can without lagging at all, then you can raise your graphics settings. If your game does lag on the lowest settings, then do not raise them as it will only get worse.