1a. Filled in lettering? Looks like those devices on the obverse and reverse had a little grease in the dies. When this happens the devices will look wider and shorter in height.

Not a big thing, unless 80% or more is prevented during the strike. The will have full rims, just like your coin. Not a premium for this coin.
1b.Besides the mint marks that were hand stamped way back when being filled in, are there any cases of In God We Trust or the dates being filled in as well? Yes on an
Grease Filled Die like yours. If the die was completely filled in, they nothing would appear where it should. If a die post was broken off the coin, the center of that device could be filled in, or even rise above the device if a piece of the die broke off below the fields.

1c. Is it a common occurrence or? Yes
Grease Fill can be common. It the
Grease Fill is huge then it is worth a premium.
2. Can a coin in general have an error on the obverse but have a fine reverse? Depends on what it is. Like the grease error, you can see if on both sides. If the coin was dented in on the obverse (damaged) Then you could see the other side of the coin bulge outwards. It the coin was struck through something during the strike, the one side can be affected and the opposite side may look normal.