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
It is possible to raise all skills to 100.
It is not possible to acquire all possible perks by reaching level 100 in every skill, since the number of perks vastly outnumbers the perks earned by leveling to that state (80).
There is no soft cap - the 80th perk is just as (relatively) easy to earn as the 1st.
However, as of the 1.9 release, you can "reset" a skill from 100 back down to 0, which means you can reach arbitrarily high levels, and finally max out your perks.