Yes, in the context of land, 'acquire' means "purchase, buy". But you wouldn't use the plain present tense. You could say, 'I acquired (= bought, purchased) this land', or 'I want to acquire (= buy, purchase) this land)', but not 'I acquire/buy/purchase this land'. Plain present tense is either habitual ("I often/repeatedly buy") or a proclamation ("I hereby make legal the purchase of this land").
You're right that I hesitated and just understood that "I acquire this land" might be said by a guy showing to a friend the land he is about to purchase (when the papers are ready and the deed is transferred).
As an English speaking member, please could you write some words about the differences b/w to acquire & to purchase/to buy.
I PMed lugovets about this but I would like natives' confirmation (I mean connotation of snobbery or dubious means).
I'm not sure that it is more formal than purchase (buy is perhaps a less formal word than purchase, so purchase is not particularly informal). The main point is that if you acquire something it comes into your possession by whatever means. It is used for abilities (such as a speaking a language) as well as material property.