In one playthrough, will it be possible for me to get every single perk and max all my skills?
With the 1.9 skyrim patch there is no limit to the levels you can achieve, so you could get all the perks in theory.
Alternatively, on pc, there are mods that can give you extra perk points. For example I use Spend Dragon Souls For Perks. Otherwise search the workshop for ‘perk’ and see what you find: e.g. Perk Potions