I'm going to address the second part of your question, since the existing answer took care of the first part.
So even if the zombies are still active years later, why so many of them? We know there are other groups in the Walking Dead universe constantly killing lots of zombies every day, at a pretty good rate. Is this ever explained?
The Kill Count Prior to Season Five:
There are statistics for zombie and human deaths on the show up to the end of season four. This site lists the kill count in seasons 1 through 4; I don't know if their numbers are exactly right, but assuming that they aren't wildly inaccurate, they are good enough for our purposes. I have taken the liberty of breaking down the data and creating a spreadsheet.
The members of the group who are listed by name in the chart have killed 956 zombies and 39 people. Other human characters have killed 229 zombies and 136 people. Zombies have killed 78 people.
The grand total:
1,185 zombies killed
253 people killed
In the comic books, and to a lesser extent on the show, Rick's group are depicted as being among the best fighters left in the world. They have repeatedly fought off much larger forces of zombies and bad guys alike. In comparison, people who aren't in Rick's group are usually zombie fodder.
The first four seasons of The Walking Dead represent perhaps 2 years of time. In 2 years, the best zombie killers around have only managed to kill 956 zombies. This does not bode well for humanity.
How Many People Versus How Many Zombies?
The blurb for the tenth issue of the comic book says:
After the ordeal Rick has endured last issue, he sets out to find safer shelter. More is learned about the zombies that now out-number us 5000 to 1, but when it comes to some things, it's better not to know. Rick begins to wonder if there is a light at the end of the tunnel his life has become. Even if there is, how can he ever expect to make it there?
In Issue #10, Carl is brought to Herschel's farm for the first time, having just been shot by Otis. This corresponds to the second episode of Season Two of the show. The second episode of Season Two takes place about a week after Rick wakes up in the hospital, and a few weeks since the outbreak began.
This means that within weeks of the beginning of the outbreak, only 0.2% of the population was still alive. What does this mean?
0.2% Humans, 99.8% Zombies:
Worldwide: 1,400,000 people against 6,998,600,000 zombies.
United States: 60,000 people against 299,940,000 zombies.
We're doomed, and trying to survive is just playing for time.