I have a trek 2100 road bike, i think the cassette is 13-28 or 13-34 The front is (53t/xxt), sometimes i feel like i want to ride faster, so i'm thinking of something like 11t, like

Shimano HG70 7-Speed 11-28 Cassette ICSHG707128

Does anyone know whether it will fit or not? I have disect another old junk mountain bike before, so i'm thinking of doing the upgrade myself this time, any tips/tricks/warning/advice from anyone? In addition, what is a good chain to go with it?

Will I wear off the 11t cassette really fast, since it is so small?