No, that is not correct
Your friends/associates are speaking from ignorance (at best), and possibly out of spite.
Per the Ecumenical Council now referred to as Vatican I (1870), papal infallibility relates to declarations made ex cathedra pertaining to faith and morals. (Catholic Encyclopedia, Infalliblity, Explanation of papal infallibility)
The Vatican Council has defined as "a divinely revealed dogma" that
"the Roman Pontiff, when he speaks ex cathedra — that is, when in the
exercise of his office as pastor and teacher of all Christians he
defines, by virtue of his supreme Apostolic authority, a doctrine of
faith or morals to be held by the whole Church — is, by reason of the
Divine assistance promised to him in blessed Peter, possessed of that
infallibility with which the Divine Redeemer wished His Church to be
endowed in defining doctrines of faith and morals; and consequently
that such definitions of the Roman Pontiff are irreformable of their
own nature (ex sese) and not by reason of the Church's consent"
(Denzinger no. 1839 — old no. 1680).
The most recent ex cathedra declaration regards the dogma of the Assumption of Mary (Apostolic Constitution of Pope Pius XII Munificentissimus Deus(AAS 42 , 760-762, 767-769). Ex cathedra declarations are rare.
Catholics believe that they have to say something like 5 to 10 of the
lords prayer and possibly a few "Hail Mary"s added to the mix per sin
depending on how "bad" it is.
That is sheer ignorance. A wide variety of things can be assigned to the penitent during confession (the sacrament of penance and reconciliation, CCC 1422- 1489) by the confessor(priest) to include actions, apologies, repayment, restitution (and much more) depending upon the sin and circumstances. Prayer is also usually assigned. Why? To turn back toward God and away from sin. (See Repentance).
Prayer is as an opening of the heart to God.
CCC 2258 WHAT IS PRAYER?
For me, prayer is a surge of the heart; it is a simple look turned
toward heaven, it is a cry of recognition and of love, embracing
both trial and joy. ~ St. Therese of Lisieux, Manuscrits
autobiographiques, C 25r.1
The point of prayer after confession is to head back into the direction of avoiding sin and near occasions of sin. This may include prayers (Hail Mary, Our Father, Glory Be, others) but just saying these prayers yourself is in no way, shape, or form the approved method of confessing and resolving mortal sin -- that requires seeking absolution through the sacrament of penance and reconciliation(confession). It may be that for a given confession penance only warrants prayer; in other cases, other penance may be assigned.