Travel /
From Wroclaw to Warsaw - is traveling long distances expensive in Poland? [7]
The train ticket you can buy online at the website intercity.pl
It is possible not earlier than a month before departure.
The problem is that it's possible to buy there only a ticket for a single train, not for a whole route with changing trains, which normally is cheaper, but still, if you buy two separate tickets online beforehand, it will be probably cheaper than a single ticket just before the departure.
For the local trains in the most of the country, the website is: biletyregionalne.pl - although in some areas they are operated by other companies, and then it's usually not possible to buy them online. But for the local trains, there is no price difference in time.
Whether it is much faster, it depends on the route. It's definitely more comfortable. Maybe except the rush time, when the trains can be crowded. It's better to travel in the middle of a week than on weekends, especially in February, when the trains might be full of school students who have just begun their winter holidays or their holidays are just about to end (they last two weeks, each week in February some regions of Poland end them and some begin). Then it might be better to take a bus. Buses usually don't take more people than the number of seats, trains do it. Even though they inform passengers about it, there is often a lot of people who risk travelling by train without a seat and the result is the train corridor full of people. This is, of course, only in special cases. Normally, the trains are much more comfortable. And the exception are EIP (Express Intercity Premium) trains, which take people only on seats.
For PolskiBus you can buy tickets on their website. For some buses they are available at e-podroznik.pl or at the website of the specific company - but in case of buses, it's often only possible to buy a ticket at the station (not always) and from the driver.
About entering Białowieża Forest on foot by yourself, I don't know, but I think it should be possible without any problem. There might be an entry fee of something like a few PLN, it's sometimes so in national parks.
Remember that February is the middle of winter in Poland. It will be cold, and, most probably, snowy. It shouldn't cause any transportation problems (there is usually a lot of problems just after the first big snowfall during the specific winter, but it is usually in December, sometimes at the end of November or at the beginning of January, and afterwards everything becomes good and the problems "magically" disappear), but still in case of a big snowfall, there might be some delays of the trains and buses. Take it into account when you are going to change between means of transport. When you are going to change between trains, when your train has a delay and you tell the conductor about it, they will either keep the train you want to change to at the station, or change your ticket to a later train. But when you are going to change from a train to a bus, from a bus to a train or between buses, it's not possible to do much with it.