What is involved in ripping out carpets and put in fake wood floors for an apartment floor overhaul?
There's no way we can offer you prices as they vary wildly based on particular products, stores, and region you live in. 

We also can't say what your landlord would or would not be willing to do. You'd have to ask them. 

As for ripping out carpet, that requires some gloves and a bit of muscle--not that hard. 

Installing flooring (be it vinyl tiles or engineered hardwood) is also fairly easy in the grand scheme of DIY projects.