I can comment on the Arcane magic thing. Arcane magic and magic of all types existed before the Sundering. Using Arcane above other types of magic was still rare, but some did. Those who did when transported to the Mortal Realm retain the ability to cast Arcane (you don't forget how to tap the primal powers). However, I have never met in playtest, or heard of in any other context, a caster from the Mortal Realm who can cast Arcane. At very least it's even more rare there.
The Church in general would consider using Arcane magic at least as evil as using any magic. There may be some who see it as more divine and pure magic, but those would probably consider it an even bigger blasphemy to use it than regular magic.
For other types of magic/whatnot, Defendi's general rule of thumb has always been that if changes in scenery would affect the usage of character abilities, we assume that with practice (maybe a little roleplaying), the character is able to adapt his powers intact to the new scene.
I assume Mana recovery in HARP is similar to Power Points in RM (Never played HARP; I'm not part of that playtest). Recovery in Heaven, Hell, and Ulcers happens at the same rate as anywhere. However, product 5 (which is coming soon) contains rules for tapping magic from Holy and Unholy ground at the cost of gaining corruption (Holy or Unholy, depending--my Gnome almost reads as having a Divine Spark as a result of drawing power off of the Holy See in Sulvican City).
For non-system questions: Our party always takes great pains to hide our origins. Our very existence is heresy. Thankfully, the first 2 people you meet when entering the Mortal Realm are those who will help you hide your origin (Brother Cathon(?) and Cardinal Gleann). You speak Divine Tongue and so do they. We roleplayed through figuring out that they were different dialects and learning to approximate the local dialect. It's not too strange to normal people because Divine Tongue is one of 2 lingua franca and they just assume your strange accent/phrasing just means you're some kind of foreigner. Same thing goes for odd cut of clothes/armor. Though, most people admired the angelic themes on our warriors' armor.
For money, the coins you bring with you are holy relics and extremely valuable. Certain groups (Sinius, Lonnuso, etc) might kill you for having them, since you obviously stole them. We gave them to Gleann for safe keeping, and he gave us local money.
The chaos your appearance might cause is softened by Gleann sheltering you and making sure you'll at least pass cursory inspection before turning you loose on the world.
At that point, as long as you don't go around shouting that you're from Heaven (or are a Gnome so no one will believe you anyway), no one should be the wiser.
I hope that helps.