There are 3 separate points or questions actually asked here that need to be addressed
- Did Jesus die on a cross or a stake?
The word stauros and its definition are the problem here. Stauros meant pole in classical Greek but not Koine Greek nor in modern Greek. It means cross. Language evolves and the meaning of words change. The word crucifixtion is Latin and means to fix to a cross. There are drawings and paintings showing the cross as a method of Roman execution such as The Alexamenos Graffito. The date of the drawing is debated but is from the 30sAD to about 200AD. Since it is mocking Christian worship it was most likely drawn by a non-Christian depicting how Jesus was crucified. Another graffito is considered the oldest known depiction of a Roman crucifixtion found in Puteoli, dated around 100 AD. You also have Josephus and Seneca the younger’s descriptions of Roman crucifixion. The cross among other instruments of execution are mentioned therein. All this evidence coupled with the Bible suggests Jesus died on a cross.
- When did the Christians start using the cross as a symbol?
The Staurogram
a standard abbreviation of the word cross in the oldest Greek manuscripts such as P66 has a picture of a cross imbedded in the word this dates prior to 150AD.
Justin martyr wrote that the cross was found in everything. The Alexamenos Graffito,mentioned earlier.mocking Christian worship places the date early as well. The evidence would suggest at least by 100AD if not before Christians revered the cross.
Tracing of Alexamenos Graffito from plaster.
Additional information here
- Finally why do Christians use a pagan symbol(the cross)?
This assumes that they borrowed this symbol from the pagans and did not derive it on their own. While the Catholic church most definitely did bring pagan beliefs in, the cross predates the Catholic Church as you know.
There is no evidence to prove they adopted the cross from someone else. Only someones theory that they did. The evidence given in the previous points show that Christians believe their savior died on a cross for their sins and that they adopted the cross as a symbol of that. Thus not from pagan sources.