This piacere is the masculine noun, meaning pleasure or favour. Look up any Italian dictionary.
Piacere alone is a (very, very common) polite greeting - 'pleasure'.
Per piacere literally means 'for pleasure' but is a (very common) polite way of saying 'please'.
A piacere literally means 'to pleasure' but is typically translated to 'as much as (you) like'.
Con piacere means 'with pleasure'.
This is the imperative, rather than the indicative, mood, so the conjugation is different for "-are" verbs: http://italian.about.com/library/weekly/aa011900a.htm
The question is: what verbal mode is ? Imperative ! ; )
Formal: per piacere (lei) aspetti ("lei" as formal you "aspetti" verb on third person singular) cinque minuti less formal: per piacere (tu) aspetta cinque minuti
Aspettare: imperative aspetta (you) aspetti (he /she/ it) aspettiamo (we) aspettate (you:more of one) aspettino (they)
Things are not quite as you seem to think.
We don't use the normal present. The imperative is a mood distinct from the present indicative; see http://italian.about.com/od/grammar/fl/The-Imperative-Mood-in-Italian.htm. Note also that the formal Lei/Loro uses the subjunctive, because the imperative is thought too rude to someone you don't know.
Only the tu form uses negative + infinitive; see http://italian.about.com/od/verbs/a/italian-imperative-negative-commands.htm.