The "-άρω" ending comes from the Italian "-are". Quite a few verbs of this kind are part of the Greek vocabulary:
μοστράρω=to show off sth
γουστάρω= to like (sth/sb) a lot
There are also verbs of Greek origin ending in "-άρω", an example being "κριτικάρω"=to criticize
The endings of the past (aorist) tense are:
1st singular: -ρα
2nd singular: -ρες
3rd singular: -ρε
1st plural: -αμε
2nd plural: -ατε
3rd plural: -αν
The verbs that get the "ε-/η-" prefix in the past (aorist) tense are those ones which are stressed on the first syllable, for example: παίζω, τρέχω, κλαίω, δείχνω etc.
On the other hand, verbs that are not stressed on the first syllable don't get that prefix, for example: πετάω, περπατάω, μιλάω, γελάω, κοιτάζω, διαβάζω, σκοράρω, μοστράρω etc. Please note that this is a rule of thumb and there are some exceptions to it. Hope this helps!