"You are very welcome!"
Is 'te nagyon szivesen' acceptable here. I know personal pronouns are not necessary.
No. "te" doesn't work here. The exact meaning of the hungarian sentence is I did it or I do it something with very pleasure.
That's good to know. By the way, you can't say ‘very pleasure’ in English; it has to be ‘much pleasure’. (Or ‘a lot of pleasure’; outside of the combinations ‘very much’ and ‘not much’, ‘much’ sounds a little old-fashioned.)
Do all native Hungarian speakers omit the pronouns? I feel it would be best to add them unless omitting them is normal and the correct way.
Omitting them is normal and the correct way. :)
Personal pronouns are only included if there's some special emphasis on them.